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A problem of positive proportion function in the second grade of junior high school, It is known that y + m is proportional to x-n, and when x = 2, y = 3; when x = 1, y = - 5. Find the value of y when x = - 1 I need it tonight
Let the scale coefficient be K, then y + M = KX kn, and kx-y = m-kn. If the numerical value is substituted, then 2k-3 = K + 5, then k = 8, y-8x = 13. So when x = - 1, y = 5
Give 20 second grade positive proportion function and a function of the problem of medium difficulty, to have the analysis process
Consolidation exercises
1、 Multiple choice questions:
1. Given that y and X + 3 are in positive proportion, and x = 1, y = 8, then the functional relationship between Y and X is ()
（A）y=8x （B）y=2x+6 （C）y=8x+6 （D）y=5x+3
2. If the line y = KX + B passes through quadrants 1, 2 and 4, then the line y = BX + K does not pass through ()
(A) Quadrant one (b) quadrant two (c) quadrant three (d) quadrant four
3. The area of the triangle formed by the line y = - 2x + 4 and the two coordinate axes is ()
（A）4 （B）6 （C）8 （D）16
4. If the analytic formula of the function between the length y (CM) of spring a and spring B and the mass x (kg) of the hanging object is y = K1X + A1 and y = k2x + A2 respectively, as shown in the figure, when the mass of the hanging object is 2kg, the length of spring a is Y1 and the length of Spring B is Y2, then the size relationship between Y1 and Y2 is ()
（A）y1>y2 （B）y1=y2
(C) Y1a, draw the graph of linear function y = BX + A and y = ax + B in the same plane rectangular coordinate system, then there are a set of values of a and B, so that one of the following four graphs is correct ()
6. If the line y = KX + B passes through the first, second and fourth quadrants, then the line y = BX + K does not pass through the () quadrant
(A) One (b) two (c) three (d) four
7. If the first-order function y = KX + 2 passes through the point (1,1), then the first-order function ()
(A) Y increases with the increase of X (b) y decreases with the increase of X
(C) The image passes through the origin (d) and does not pass through the second quadrant
8. No matter what the real number of M is, the intersection of the line y = x + 2M and y = - x + 4 cannot be in ()
(A) Quadrant 1 (b) quadrant 2 (c) quadrant 3 (d) quadrant 4
9. To get the image of y = - x-4, the line y = - x ()
(A) Pan 4 units to the left (b) pan 4 units to the right
(C) 4 units up (d) 4 units down
10. If y in the function y = (m-5) x + (4m + 1) X2 (M is a constant) is positively proportional to x, then the value of M is ()
（A）m>- （B）m>5 （C）m=- （D）m=5
11. If the intersection of y = 3x-1 and y = x-k is in the fourth quadrant, then the value range of K is ()
(A) K < (b) 1 or K
The cost of holding a table tennis match in a certain place is y yuan, which includes two parts: one is B yuan, which is a fixed cost, such as renting the playing field, and the other is in direct proportion to the number of players x (people)
=1600, when x = 30, y = 2000
1. If there are 50 athletes participating in the competition, and all the expenses are shared by the athletes, how much will each athlete have to pay?
Write down the process,
Let X be a positive proportion to the number of people participating in the competition, then y = ax + B when x = 20, y = 1600, 1600 = 20A + B formula 1 when x = 30, y = 2000, 2000 = 30A + B formula 2 use formula 2-formula 1, there are: 400 = 10A, a = 40, substitute a = 40 into formula 11600 = 800 + BB = 800, so y = 40x + 800 when x = 50, y = 2000 + 8
RELATED INFORMATIONS
- 1. Proportion is divided into positive proportion and negative proportion
- 2. Fill in the blanks and judgment questions of positive and negative proportion exercises, 1. 35: () = 20 △ 16 = = ()% = () (fill in decimal) 2. Because x = 2Y, X: y = (): (), X is proportional to y 3. The side area of a cylinder is fixed, and the circumference of its bottom is proportional to its height 4. The circumference of a circle is proportional to its radius 5. The ratio of edge length of two cubes is 1:2, and the ratio of their volume is (): () 6. With the same tiles, shop 64 square meters to 320, as such, shop 20 square meters to () pieces 1. The ratio of number a to number B is 3:4, and the number a is 3 / 4 of the number B 2. When 10 grams of pesticide are dissolved in 90 grams of water, the ratio of pesticide to water is 9:1 3. In the 800 meter race, the speed of an athlete is inversely proportional to the time spent 4. A parallelogram has a certain area, and its base and height are in direct proportion 5. The weight of peanut is proportional to the weight of peanut oil 6. If the actual distance is constant, the distance on the map is in direct proportion to the scale 7. The volume of a cube is constant, and the area of its base is inversely proportional to its height 8. The total amount of subscription to Hebi daily is proportional to the number of copies 9. When the total number of parts is fixed, the number of produced parts is inversely proportional to the number of unproductive parts 10. A person's weight is directly proportional to his height 11. The circumference of a rectangle is fixed, and its length and width are in inverse proportion 12. The total amount of water is fixed, and the amount of water used is inversely proportional to the amount of water remaining 13. The radius of a circle is proportional to its area 14. A scale is a ratio, so it has no unit
- 3. Mathematical inverse proportional function It is planned to build a rectangular lawn with an area of 600. The functional relationship between Y length and x width? Y: x = 3:2, what are the length and width respectively? It's all wrong
- 4. A problem of inverse proportion function As shown in the figure, the image of the positive scale function y = 1 / 2 x and the image of the inverse scale function y = K / X (K ≠ 0) in the first quadrant intersect at point a, cross point a to make a vertical line of the X axis, the perpendicular foot is m, and the known area of △ OAM is 1, (1) Finding the analytic expression of inverse proportion function (2) If B is an inverse scale function, and the abscissa of point B is 1 at the point on the first quadrant image (point B does not coincide with point a), find a point P on the X axis to minimize PA + Pb
- 5. Judging inverse proportion function If the area of the trapezoid is fixed, is the median line inversely proportional to the height?
- 6. A judgment question A project can be completed in 6 days with the cooperation of Party A and Party B. If Party A does it alone in 10 days, then Party B does it alone in 15 days
- 7. Ten mathematical judgment questions 1. An equation with unknowns is called an equation () 2. N is a natural number, and 2n is an even number () 3. Because 22 = 2 × 2, A2 = a × 2 () 4. 56-x < 0.7 is not equation () 5、c +c=2c,a×a=2a.（ ） 6. An equation must be an equation, and an equation does not have to be an equation 7、a²＞a×2 .( ) 8. When a = 3, the cube of a = a × 3 9. The process of solving an equation is called solving an equation 10. 4m-12 = 0 is the equation
- 8. As shown in the figure, it is known that the image of the inverse scale function Y1 = K1X and the image of the primary function y2 = k2x + B intersect at two points a and B, and a (2, n), B (- 1, - 2). (1) find the relationship between the inverse scale function and the primary function; (2) use the image to write directly when x is in what range, Y1 > Y2
- 9. It is known that y is the inverse proportional function of X. when x = 3, y = 2, then the functional relation between Y and X is______ ．
- 10. As shown in the figure, points a (m, M + 1) and B (M + 3, m-1) are all on the image of inverse scale function y = KX. (1) find the value of M and K; (2) if M is a point on the x-axis, n is a point on the y-axis, and the quadrilateral with points a, B, m and N as vertices is a parallelogram, try to find the functional expression of straight line Mn
- 11. If the images of positive scale function and linear function pass through point m (3,4) If the images of the positive scale function and the first-order function pass through the point m (3,4), and the area between the images of the positive scale function and the first-order function and the Y axis is equal to 15 / 2, the analytic expressions of the two functions are obtained
- 12. Given that the image of positive scale function y = KX passes through (2,3a) and (a, - 6) (a is greater than 0), the value of X when y = 3 is obtained
- 13. The expression of positive scale function of image passing through (1,2) is______ ．
- 14. When the image with positive scale function y = 5x passes through the first quadrant and the second quadrant, point (0,) and point (1,) are on the image, y The image with positive scale function y = 5x passes through the second image Point (0,) and point (1,) are in their image Y increases with the increase of X?
- 15. If the inverse scale function y = KX passes through (- 3,2), then the image______ Quadrant
- 16. Given the function y = (M-3) x ^ (m ^ 2-10), when what is the value of M, it is an inverse scale function? In which quadrant is his image located
- 17. Let the function y = (m-2) x * M-4 be an inverse scale function. (1) find the value of M. (2) draw the image of this function and point out which quadrant is its image located? Let y = (m-2) x * M-4 be an inverse proportional function (1) Finding the value of M (2) Draw an image of this function and point out which quadrants its image is in? (3) If the line y = KX intersects with the image of this function at two points a and B, and the ordinate of point a is 2, it is the solution set of the inequality (m-2) x * M-4 > KX about X
- 18. Given a positive proportional function and a first-order function, their images pass through the point P (- 3,3), and the image of the first-order function intersects with the Y axis at the point Q (0, - 2), the analytic expressions of the two functions are obtained
- 19. A function image translation problem How is the image of F (x) translated from the image of F (x-1)? Let's take an example,
- 20. What is the relationship between the image translation of linear function and X and K?