Question

What is the y-intercept of the line that passes through the points (-3,8) and (1,6)? Convert the answer to a decimal, if necessary.

Answer 1

y-intercept =6.5

Explanation:

First , lets find the slope

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\\\\\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(1,\:6\right)\\m=(6-8)/(1-\left(-3\right))\\\\Refine\\m=-(1)/(2)`

`(-3,8) =(x_1,y_1)\\m =-(1)/(2) \\\\`

Plug in values point point slope form

`y-y_1=m(x-x_1)\\\\y -8=-(1)/(2) (x-(-3))\\\\y - 8 =-(1)/(2) (x+3)\\\\y -8= -(1)/(2) x -(3)/(2) \\\\y =-(1)/(2) x - (3)/(2) +8\\\\y = -(1)/(2)x +(13)/(2) \\y =\:mx\:+\:b`

Where b = y-intercept

y-intercept =
`(13)/(2)`

Answer 2

6.5

Explanation:

The midpoint of the line is (-1,7). If you draw a line between that and (1.6), you’ll pass through the y-axis at 6.5.