Question

Write the point slope form of the equation of the line using the point (-4,-2)

Answer 1

`y + 2 = (5)/(4) (x + 4)`

Explanation:

1) First, find the slope of the line. Take two points the line intersects and use them for the slope formula,
`(y_2-y_1)/(x_2-x_1)`. We already know the line intersects (-4, -2). Just choose any one of the points you can see the line intersecting (in this case, I chose (0,3)) and plug in its values, too. Then solve:

`((3)-(-2))/((0)-(-4)) \\(3+2)/(0+4) \\(5)/(4)`

So, the slope is
`(5)/(4)`.

2) Now that you have the slope, plug in values for the point-slope formula,
`y - y_1 = m (x - x_1)`. In order to write a linear equation with it, the
`x_1`,
`y_1`, and
`m` have to be substituted for with real values. The
`m` represents the slope - which means that we should place
`(5)/(4)` there. The
`x_1` and
`y_1` represent the x and y values of a point - and the questions wants us to use (-4, -2), so substitute -4 for
`x_1` and -2 for
`y_1`:

`y-(-2) = (5)/(4) (x - (-4))\\y + 2 = (5)/(4) (x + 4)\\`

Thus, the answer is
`y + 2 = (5)/(4) (x + 4)`.