Question

The points (2,-4), (x, y), A, and B all lie on the line. Find an equation relating and

y.
2
→
0
-1
N
-3
بنا
-4
5
(2,-4)
2
3
4
(x,x)
F
fun
9
A
100
8
a
B
3
C
11

Answer 1

To find an equation relating x and y, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Given the points (2, -4) and (x, y), we can find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (2, -4) and (x, y) into the formula, we have:

m = (y - (-4)) / (x - 2)

Simplifying further:

m = (y + 4) / (x - 2)

Now, we need to find the value of m. Let's use the coordinates (0, -1) and (2, -4) to calculate the slope:

m = (-4 - (-1)) / (2 - 0)

m = (-4 + 1) / 2

m = -3 / 2

Now that we have the slope (m = -3/2), we can substitute it into the slope-intercept form equation:

y = (-3/2)x + b

To find the value of b (the y-intercept), we can substitute the coordinates (2, -4) into the equation:

-4 = (-3/2)(2) + b

-4 = -3 + b

b = -4 + 3

b = -1

Therefore, the equation relating x and y is:

y = (-3/2)x - 1