Question

Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form

Answer 1

slope = (10 -5)/(2+3) = 5/5=1

y = mx + b
5 = 1(-3) + b
b =8

so equation y = x +8

answer: y = x + 8(first choice)

Answer 2

The slope-intercept form is
`y=x+8`

Explanation:

Given points are (-3, 5) and (2,10). Now, we have to find the equation of the line that passes through these points in slope-intercept form.

Equation of line passing through the point (x', y') can be written as

`y-y'=m(x-x')` where m is
`(y_(2)-y_(1))/(x_(2)-x_(1))`

Hence, the equation can be written as
`(y-5)=(10-5)/(2-(-3))(x-(-3))`

⇒
`y-5=(5)/(5)(x+3)`

⇒
`y=x+3+5`

⇒
`y=x+8`

which is slope-intercept form where slope is 1 and intercept is 8 by comparing with y=mx+c