Make a straight line L through point a (- 5, - 4) so that it intersects with two coordinate axes and the area of the triangle enclosed by the two axes is 5. The equation of L is obtained There should be a specific process

Make a straight line L through point a (- 5, - 4) so that it intersects with two coordinate axes and the area of the triangle enclosed by the two axes is 5. The equation of L is obtained There should be a specific process

Let the linear equation be y = KX + B and the area of the triangle bounded by two axes be = | - B / K | * | - B | = 5 | - B / K | * | - B | = 5, and the square of both sides is B ^ 4 / K ^ 2 = 25, because the line passing through point a (- 5, - 4) is - 4 = - 5K + B, then k = (4 + b) / 5B ^ 4 / K ^ 2 = B ^ 4 / [(4 + b) ^ 2 / 25] = 25B ^ 4 = (4 + b) ^ 2
Urgently seeking 100 mixed operation problems of rational numbers at the first level of junior high school ～
The mixed operation of addition, subtraction, multiplication and division does not need to be too long, such as 23 * (- 21 * 14) + (12 / 3) * 3
Remember 100 thanks
Addition and subtraction are mutual, multiplication and division are mutual（
Addition and subtraction are reciprocal operations, multiplication and division are reciprocal operations
Inverse operation
Inverse operation
Given that the line L intersects two coordinate axes and the central coordinates of the line segment cut by the two coordinate axes are (2,4), then the equation of the line L is?
Because: the line L intersects the two coordinate axes, and the central coordinates of the line segment cut by the two coordinate axes are (2,4),
So: (x + 0) / 2 = 2, the solution is: x = 4
So: (0 + y) / 2 = 4, the solution is y = 8
Let the linear equation be y = KX + B
Then: B = 8, k = - 2
So: the equation of line L is y = - 2x + 8
On the first problem of rational number
X-1 + 2-3 + 4 -. + 100, find the value of X
100-99 + 98-97 +...+ 2-1 =1+1+.+1
=50
There are 50 pairs of 100 numbers, so
X=50
The nature of subtraction is represented by letters
a-b=c
a-c=b
b+c=a
The area of the triangle formed by a line and two coordinate axes is 2, and the absolute value of the difference between the two intercepts is 3
Let: the two intercept of a straight line on the X and Y axes be: X, Y. then: X * y = 2 * 2 = 4; X + y = 3. Or X-Y = 3. Solve the above equation: x = + 1, y = + 4; X = + 1, y = - 4; X = - 1, y = + 4; X = + 4, y = + 1; X = - 4, y = - 1; X = - 4, y = - 1; X = - 4, y = + 1; X = - 4, y = - 1
Solution: let the intercept of the line and X, Y axis be respectively: X, y, so: 1 / 2XY = 2 -------- 1
|Formula X-Y | = 3 -------- 2
After Formula 1 x = 1 / y is brought into formula 2, the square solution on both sides of the equation is y = 1 or y = 4, x = 4 or x = 1
The following problem is simple. There are too many straight lines that satisfy these two conditions. There are at least eight lines. Just set... First
Solution: let the intercept of the line and X, Y axis be respectively: X, y, so: 1 / 2XY = 2 -------- 1
|Formula X-Y | = 3 -------- 2
After Formula 1 x = 1 / y is brought into formula 2, the square solution on both sides of the equation is y = 1 or y = 4, x = 4 or x = 1
The following problem is simple. There are too many straight lines satisfying these two conditions. There are at least eight lines. Let's first set the linear equation as: y = ax + B, then (0,4) (1,0); (0, - 4) (- 1,0).... You can get it after 8 groups of points are brought in
Eight equations with + 4, - 4, + 1, - 1 as intersections respectively
On rational numbers in the first day of junior high school
A little more
Due to technical problems, my absolute value is expressed as "/ /". 1. If the rational number / A / A / A + / B / b = 0, then / AB / AB is equal to? 2. Compare the following numbers and connect them with less than sign. / sub half /, / positive five seventh /, / 0 /, - / - 3 /, - ()-
What is the nature of subtraction
Subtraction has the following operational properties: 1. A number minus a number, plus the same number, a number remains unchanged, that is, (a-b) + B = A2. A number plus a number, minus the same number, a number remains unchanged, that is, (a + b) - B = A3. The sum of N numbers minus a number can be subtracted from any addend
If a line L passes through point m (1,1), and the area of the triangle formed by the first quadrant and two coordinate axes is the smallest, the equation of line l can be solved
Let the linear equation be:
x/a+y/b=1,a>0,b>0
Satisfy: 1 / A + 1 / b = 1 > = 2 √ 1 / AB
therefore
AB > = 4 (take equal sign when a = b = 2)
therefore
Area s = 1 / 2 * ab
Its minimum value is 1 / 2 * 4 = 2
The equation is
x/2+y/2=1
Namely
y=-x+2.
Let the intersection points of the intersection coordinates of the straight lines be (x, 0) and (0, y) respectively, then the area is XY, which is rounded off by the formula: 2XY = 2 or K + 1 / K0)
So when smin = 1 / 2 (2 + 2) = 2, k = 1 / K, k = - 1
So the equation of L is Y-1 = - 1 (x-1), that is y = - x + 2
Let y = KX + B and pass through point m (1,1), then there is:
k+b=1................................................1
In the first quadrant, the area of the triangle is the smallest
K0
S = - B ^ 2 / 2K, i.e. k = - B ^ 2 / 2S...... 2, substitute it into 1 to get:
-B ^ 2 / 2S + B = 1, i.e. B ^ 2-2bs +... Expansion
Let y = KX + B and pass through point m (1,1), then there is:
k+b=1................................................1
In the first quadrant, the area of the triangle is the smallest
K0
S = - B ^ 2 / 2K, i.e. k = - B ^ 2 / 2S...... 2, substitute it into 1 to get:
-B ^ 2 / 2S + B = 1, that is, B ^ 2-2bs + 2S = 0
Δ ≥ 0, i.e
4S ^ 2-8s ≥ 0: s ≥ 2
So s = 2, B = 2, k = - 1
So the equation of line L is y = - x + 2
The equation of line L: y = - x + 2
analysis:
1. Let y = ax + B be the function of the line L. since l passes through M, the coordinate of M is substituted into the function of Y,
We get a + B = 1, B = 1-A.
2. If the x-axis and Y-axis of L intersection are - B / A and B respectively, then the triangle area is
S = 1 / 2 × B × (- B / a) = - (1 / 2) × a + 1-1 / 2a, then we can find out a = plus or minus 1 by square formula, but because l is over the expansion of
The equation of line L: y = - x + 2
analysis:
1. Let y = ax + B be the function of the line L. since l passes through M, the coordinate of M is substituted into the function of Y,
We get a + B = 1, B = 1-A.
2. If the x-axis and Y-axis of L intersection are - B / A and B respectively, then the triangle area is
S = 1 / 2 × B × (- B / a) = - (1 / 2) × a + 1-1 / 2a, then we can find out a = plus or minus 1 by square formula, but since l passes through the first quadrant, a