Question

Find the line's slope and a point on the line. y-1=-3/2(x+7)

Answer 1

The slope is m=-3/2 and one point on the line is (-1, -8)

1) Since we have this equation written in the Point-Slope Form, we can state that:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-1=-(3)/(2)(x+7) \end{gathered}`

Making a comparison, we can state that the slope m is -3/2.

2) Let's find now a point that belongs to this line. For that, we can set a table putting in some values for x, to find the corresponding y-coordinate:

Firstly, we can rewrite into the Slope-Intercept form to make it easier to find out a point.

`\begin{gathered} y-1=-(3)/(2)(x+7) \\ y=-(3)/(2)(x+7)+1 \\ y=-(3)/(2)x-(21)/(2)+1 \\ y=-(3)/(2)x-(21)/(2)+(2)/(2) \\ y=-(3)/(2)x-(19)/(2) \end{gathered}`

Now, we can fill in a table, and plug x= -1 into the equation:

x | y=-3/2x -19/2

-1 | y=-3/2(-1) -19/2= -8

3) Hence, the slope is m=-3/2 and one point on the line is (-1, -8)