Question

Complete the equation of the line through (2,1)(2,1)left parenthesis, 2, comma, 1, right parenthesis and (5,-8)(5,−8)

Answer 1

Answer:

$y=-3x+7$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

$m=\displaystyle \frac{y_2-y_1}{x_2-x_1}$ where two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the points (2,1) and (5,-8):

$m=\displaystyle \frac{-8-1}{5-2}\\\\m=\displaystyle \frac{-9}{3}\\\\m=-3$

Therefore, the slope of the line is -3. Plug this into  $y=mx+b$ as m:

$y=-3x+b$

2) Determine the y-intercept (b)

$y=3x+b$

Plug in one of the given points and solve for b:

$1=-3(2)+b\\1=-6+b\\b=7$

Therefore, the y-intercept is 7. Plug this back into $y=-3x+b$:

$y=-3x+7$

I hope this helps!