Question

Find an equation of the line passing through the pair of points. Write the equation in slope-intercept form. (2,8), and (8,2)

Answer 1

Answer:

$y=-x+10$

Step-by-step explanation:

Hi there!

Slope intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Find the slope (m)

$m=\frac{y_2-y_1}{x_2-x_1}$ where the two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (2,8),and (8,2)

​$m=\frac{2-8}{8-2}\\m=\frac{-6}{6}\\m=-1$

Therefore, the slope of the line is -1. Plug this into  $y=mx+b$:

$y=-x+b$

2) Find the y-intercept (b)

$y=-x+b$

Plug in a given point and solve for b

$8=-2+b$

Add 2 to both sides

$8+2=-2+b+2\\10=b$

Therefore, the y-intercept is 10. Plug this back into $y=-x+b$:

$y=-x+10$

I hope this helps!