Question

Find the equation for the line that passes through the points ( 7 , 2 ) and ( 10 , − 6 ) . Give your answer in slope intercept form

Answer 1

Answer:

y  =  $\frac{-8}{3}$x + $\frac{62}{3}$

Step-by-step explanation:

Use slope formula.

then substitute slope for m in y = mx + b

pick a set of coordinates and substitute them in for x and y.

Solve for b

Answer 2

Answer:

$y=-\frac{8}{3}x+\frac{62}{3}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

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

Plug in the points (7,2) and (10,-6)

$m=\frac{2-(-6)}{7-10}\\m=\frac{2+6}{7-10}\\m=\frac{8}{-3}$

Therefore, the slope of the line is $-\frac{8}{3}$. Plug this into $y=mx+b$:

$y=-\frac{8}{3}x+b$

2) Determine the y-intercept (b)

$y=-\frac{8}{3}x+b$

Plug in one of the given points and solve for b

$2=-\frac{8}{3}(7)+b\\2=-\frac{56}{3}+b$

Add $\frac{56}{3}$ to both sides to isolate b

$2+\frac{56}{3}=-\frac{56}{3}+b+\frac{56}{3}\\\frac{62}{3}=b$

Therefore, the y-intercept is $\frac{62}{3}$. Plug this back into $y=-\frac{8}{3}x+b$:

$y=-\frac{8}{3}x+\frac{62}{3}$

I hope this helps!