Question

Write an equation for the line that passes through the points (-4,3) and -8,5)​

Answer 1

`y=\displaystyle- (1)/(2) x+1`

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 the line crosses the y-axis).

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 given points (-4,3) and (-8,5)​:

`m=\displaystyle(3-5)/(-4-(-8))\\\\m=\displaystyle(-2)/(-4+8)\\\\m=\displaystyle(-2)/(4)\\\\m=\displaystyle- (1)/(2)`

Therefore, the slope of the line is
`\displaystyle- (1)/(2)`. Plug this into
`y=mx+b`:

`y=\displaystyle- (1)/(2) x+b`

2) Determine the y-intercept (b)

`y=\displaystyle- (1)/(2) x+b`

Plug in one of the points and solve for b:

`3=\displaystyle- (1)/(2) (-4)+b\\\\3=2+b\\b=1`

Therefore, the y-intercept is 1. Plug this back into the equation:

`y=\displaystyle- (1)/(2) x+1`

I hope this helps!