Question

Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7. (hint: NOT y=3x-13)

Answer 1

To find the equation of the line, we are going to use the point-slope form, which is listed below:

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

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

You may notice that we have a point, but no slope is given to us. However, the problem states that the line is parallel to the equation $y = 3x + 7$, which means that it has the same slope as this line, which is 3. (Remember that this line is set up in $y = mx + b$ form, where $m$ is the slope)

Thus, we can now insert our values into the point-slope formula to find the equation of our line.

$(y + 1) = 3(x - 4)$

$(y + 1) = 3x - 12$

$y = 3x - 13$

The problem made it clear that it didn't want the form $y = 3x - 13$, so let's put it in standard form:

$y = 3x - 13$

$3x - y = 13$

The equation of our line is $\boxed{3x - y = 13}$.