If the image of a linear function passes through point a (- 2, - 1) and is parallel to the line y = 2x-1, the analytic expression of the function is?

If the image of a linear function passes through point a (- 2, - 1) and is parallel to the line y = 2x-1, the analytic expression of the function is?

If the image of a linear function is parallel to the line y = 2x-1, then the analytic expression of the function can be set as y = 2x + B
Substituting point a (- 2, - 1), we get: - 4 + B = - 1
The solution is: B = 3
Therefore, the analytic formula of the first-order function is y = 2x + 3

Given that the image of the first-order function passes through the intersection of the line y = - x + 1 and the X axis, and the ordinate of the intersection with the Y axis is - 2, the expression of the first-order function can be obtained?

The intersection of line y = - x + 1 and X axis
y=0
x=1
The intersection point (1,0) of the line y = - x + 1 and X axis
The ordinate of the intersection point with y axis is - 2
Intersection with y axis (0, - 2)
The expression of this linear function is y = KX + B
Substituting points (0, - 2), (1,0) into
b=-2
0=k+b
k=2
The expression of this linear function is y = 2x-2

The graph of a function passes through the point P (1,2) and the intersection point with the straight line y = 2x + 3 is on the y-axis
The graph of a function passes through the point P (1,2) and the intersection point with the straight line y = 2x + 3 is on the y-axis

Let the expression of the function be y = KX + B ∵ passing through the point (1,2) (0,3) ∵ 2 = K + B 3 = B ∵ k = - 1, B = 3

Given that the image of a function of degree passes through a (0,6), and the parallel line y = - 2x, the analytic expression of this number is obtained

Let the analytic expression of the line be y = - 2x + C
Straight line passing a (0,6)
Then 6 = C
So y = - 2x + 6, that is, 2x + y-6 = 0

The graph of a function of degree is known to pass through a (0,6) and parallel to the straight line y = - 2x

Because parallel to the line y = - 2x
So the slope of the line is k = - 2
Passing point a (0,6)
So the line is y-6 = - 2 * (x-0)
That is y = - 2x + 6

It is known that the image of a linear function passes through a (- 2. - 3) and is parallel to the straight line y = 2x
(1) find the expression of this linear function
(2) try to judge whether the point P (- 1.1) is on the graph of this function

A:
1）
The linear function y = KX + B passes through the point a (- 2, - 3) and is parallel to the line y = 2x
The results are as follows:
k=2
-2k+b=-3
The solution is: k = 2, B = 1
So: the linear function is y = 2x + 1
2）
The point P (- 1,1), x = - 1 is substituted into the straight line to get y = - 2 + 1 = - 1
So: the point P (- 1,1) is not on the line y = 2x + 1

If the image of a function is parallel to y = 2x and passes through point a (- 4,2), the expression of the function is

Let y = 2x + B and substitute a (- 4,2) to get b = 10, so y = 2x + 10

If the distance between the image of the linear function y = KX + 3 and the two intersections of the coordinate axis is 5, then the value of K is 0______ ．

Let x = 0 and y = 3 in y = KX + 3, then the intersection coordinates of function and Y axis are: (0, 3); let the intersection coordinates of function and X axis be (a, 0), according to Pythagorean theorem, A2 + 32 = 25 and a = ± 4; when a = 4, substitute (4, 0) into y = KX + 3 and K = - 34; when a = - 4, substitute (- 4, 0) into y = KX + 3 and K = 34

If the distance between the image of the linear function y = KX + 3 and the two intersections of the coordinate axis is 5, then the value of K is

x=0;y=3;
y=0;x=-3/k;
∴√（9/k²+9）=5;
9/k²+9=25;
9/k²=16;
k²=9/16;
k=±3/4;
If you don't understand this question, you can ask,

If the distance between the image of the linear function y = KX + 3 and the two intersections of the coordinate axis is 5, then the value of K is 0______ ．

Let x = 0 and y = 3 in y = KX + 3, then the intersection coordinates of function and Y axis are: (0, 3); let the intersection coordinates of function and X axis be (a, 0), according to Pythagorean theorem, A2 + 32 = 25 and a = ± 4; when a = 4, substitute (4, 0) into y = KX + 3 and K = - 34; when a = - 4, substitute (- 4, 0) into y = KX + 3 and K = 34