Question

The equation of the graphed line in slope-point form using (2,-1) is ___, and it’s equation in slope-intercept form is ___.

Answer 1

[see below]

For "slope-point" form:

Slope point (also called "Point-slope") form is:
`y-y_1=m(x-x_1)`

`(x_1,y_1)\text{ -Coordinate} \\m\text{ -Slope}`

Finding the Slope:

We need to find the slope of the line given.

Slope is:
`m=(y2_-y1)/(x_2-x_1)`

We are given the points (2,-1) and (-2,-2).

`m=(-2-(-1))/(-2-2)=(-1)/(-4)=\boxed{(1)/(4)}`

The slope of the line is 1/4.

Creating the Point-Slope Equation:

Replace 'm' with 1/4 and '(x1, y1)' with (2, -1).

`y-y_1=m(x-x_1)\rightarrow\boxed{y+1=(1)/(4)(x-2)}`

`\text{The equation of the graphed line in slope-point form using (2,-1) is:}\\y+1=(1)/(4)(x-2)`

Creating the Slope Intercept Form Equation:

Slope intercept form is:
`y=mx+b`

We can convert our point slope equation into slope intercept form.

`y+1=1/4(x-2)\\\\y+1=1/4x-0.5 \leftarrow \text{Distribute}\\y+1-1=1/4x-0.5-1 \leftarrow \text{Subtraction Property of Equality}\\\boxed{y=(1)/(4)x-1.5}`

The equation of the line in slope intercept form is:
`y=(1)/(4)x-1.5` OR
`y=(1)/(4)x-(3)/(2)`.