Question

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

Answer 1

Answer:

An equation relating x and y is:

y = 3/4x - 5.5

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

Given the points

(2, -4), (x, y), A(6, -1), and B(10, 2)

Taking any two points let say A(6, -1), and B(10, 2) to determine the slope

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(6,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:2\right)$

$m=\frac{2-\left(-1\right)}{10-6}$

Refine

$m=\frac{3}{4}$

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = -5.5

Thus, the y-intercept b = -5.5

Thus, substituting b = -5.5 and m = 3/4 in the slope-intercept form of the line equation

y = mx+b

y = 3/4x + (-5.5)

y = 3/4x - 5.5

Therefore, an equation relating x and y is:

y = 3/4x - 5.5