Question

How do you write an equation in slope intercept form given (-2, 3) and is parallel to 3x + 2y = 10?

Answer 1

`y-3=-3/2(x+2)`

Explanation:

Things to Remember

1. A line with the general form: `color(white)("XXX")Ax+By=C`
   has a slope of `color(white)("XXX")m=-A/B`

2. All parallel lines have the same slope.

3. The slope-point form for a line with slope `m` through a point `(a,b)` is
   `color(white)("XXX")y-b=m(x-a)`

Therefore for this example

a. `3x+2y=10` has a slope of `m=-3/2`

b. All lines parallel to `3x+2y=10` have a slope of `m=-3/2`

c. The slope point form for a line with slope `m=-3/2` through the point `(-2,3)` is
`color(white)("XXX")y-3=-3/2(x+2)`