Question

The line y-5= 9/7(x + 4) is graphed in the coordinate plane. Complete the sentences below describing this process. By inspecting the equation, the graph of the line has a slope of.............

Answer 1

We have a line with equation:

`y-5=(9)/(7)(x+4)`

The expression of the line is the slope-point form, that is:

`y-y_0=m(x-x_0)`

where (x0,y0) is a point of the line and m is the slope.

As in this case, m = 9/7, then the slope is 9/7.

By inspecting the equation, the graph of the line has a slope of 9/7.

We also know that (x0,y0) = (-4, 5), that belong to the line.

By inspecting the equation the graph of the line passes through the point (-4, 5).

To find the value of y(3) we replace x with the value 3:

`\begin{gathered} y-5=(9)/(7)(3+4)=(9)/(7)\cdot7=9 \\ y-5=9 \\ y=9+5 \\ y=14 \end{gathered}`

The value of y(3) is 14. The point is (3, 14).