Question

an equation of the line that passes through the given point and is parallel to the graph of the given equation

(1) (2-1) and y=5x-2

(2) (0-5) and y=9x

Answer 1

To construct the equations for these lines, we are going to use the point-slope formula, which is:

$(y - y_1) = m(x - x_1)$

• $m$ is the slope of the line
• $(x_1, y_1)$ is a point on the line

1)

In this case, our point is (2, -1) and our line has a slope of 5. (Remember that the line is parallel, meaning that it has the same slope as the given line. Since the line is in the y = mx + b format, we could easily pick out the slope m as being 5.)

Thus, we can "plug in" what we know into our formula to find the equation of our line:

$(y + 1) = 5(x - 2)$

$(y + 1) = 5x - 10$

$y = 5x - 11$

2)

We are going to do the same thing, except our point is now (0, -5) and our slope is now 9.

$(y + 5) = 9(x - 0)$

$y = 9x - 5$

Our equations are:

1) y = 5x - 11

2) y = 9x - 5