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

`y=-3x+7`

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 (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 (-8-1)/(5-2)\\\\m=\displaystyle (-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!