Question

Find the equation of a line that is parallel to this line and passes through the point (-3,1)

Answer 1

Two possible equations:

Point-slope form is
`y-1=-(2)/(3) (x+3)`

Slope-Intercept form is
`y=-(2)/(3)x+-1`

Explanation:

So to start we need to know what makes a line parallel. In an equation we know that for lines to be parallel they must have the same slope(
`m`).

Then, we need to know the slope-intercept form of an equation. The point slope form is
`y-y1=m(x-x1)` where
`m` is the slope of the line and
`y1` and
`x1` represent the point on the graph. This is the equation we'll use for the line.

So now that we understand what we need to find, we need to find the slope of the existing line. To do this we use the equation
`m=(y2-y1)/(x2-x1)`. We can plug in the points (-2,3) and (1,1) on the graph to get
`m=(1-3)/(1+2)`. When we simplify this we get
`m=-(2)/(3)` so we know our slope is
`-(2)/(3)`. Lastly, all we need to do is plug the slope and the new point into our point slope equation to get
`y-1=-(2)/(3) (x+3)`.

If you needed to go further and put this into slope-intercept form, you could solve the equation for y to get
`y=-(2)/(3)x+-1`