Question

Enter the equation of the line in slope-intercept form. Slope is -1/2, and (-9,4) is on the line. The equation of the line is y=

Answer 1

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

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Plug in the slope (m)

We're given that the slope is
`\displaystyle-(1)/(2)`. In
`y=mx+b`, replace m with
`\displaystyle-(1)/(2)`:

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

2) Determine the y-intercept (b)

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

We're given the point (-9,4). Plug this point into the equation as
`(x,y)` and solve for b:

`4=\displaystyle-(1)/(2)(-9)+b\\\\4=\displaystyle(9)/(2)+b`

Subtract
`\displaystyle(9)/(2)` from both sides to isolate b:

`4-\displaystyle(9)/(2)=\displaystyle(9)/(2)+b- \displaystyle(9)/(2)\\\\\displaystyle-(1)/(2) = b`

Therefore, the y-intercept is
`\displaystyle-(1)/(2)`. Plug this back into
`y=\displaystyle-(1)/(2)x+b` as b:

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

I hope this helps!