Question

Find the point-slope equation for

the line that passes through the
points (7, -21) and (-4, 23). Use
the first point in your equation.
y- [?] = [ ](x-[])

Answer 1

`y+21 = -4(x-7)`

Explanation:

1) First, find the slope of the line between the two points. Use the slope formula,
`m = (y_2-y_1)/(x_2-x_1)`. Substitute the x and y values of (7, -21) and (-4, 23) into the formula and simplify:

`m = ((23)-(-21))/((-4)-(7)) \\m = (23+21)/(-4-7)\\m = (44)/(-11)\\m = -4`

So, the slope of the line is -4.

2) Now we have all the information we need. To write the equation of the line, use the point-slope formula
`y-y_1 = m (x-x_1)` and substitute values for
`m`,
`x_1`, and
`y_1`.

Since
`m` represents the slope, substitute -4 in its place. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, substitute the x and y values of (7, -21) into the equation as well. This gives the following answer:

`y+21 = -4(x-7)`