Answer
$4x - y = -2$
Work Step by Step
The equation given is in standard form, so we want to change it to slope-intercept form to be able to see what the slope is. The slope-intercept form is given by the formula:
$y = mx + b$
To isolate the $y$ term, let us subtract the $x$ term from each side of the equation:
$-y = -4x + 5$
Divide all terms on each side by $-1$ to isolate $y$:
$y = 4x - 5$
This line has a slope of $4$; therefore, the equation of the line we want to find also has a slope of $4$.
We can get the y-intercept of the equation we are looking for from the second equation we are given. Let us also rewrite this equation in slope-intercept form to find the y-intercept. First, we add the $x$ term to both sides to isolate the $y$ term:
$3y = 13x + 6$
Divide both sides by $3$ to isolate $y$:
$y = \frac{13}{3}x + 2$
We see that the y-intercept of this graph is $2$; therefore, the y-intercept of the equation of the line we are looking for is also $2$.
Now that we have both the slope and y-intercept of the line we are looking for, we can plug in these values into the slope-intercept form:
$y = 4x + 2$
We need to rewrite this equation in standard form ($Ax + By = C$).
First, let us subtract $4x$ from each side:
$-4x + y = 2$
Let's divide all terms by $-1$ so that the $x$ term is not negative:
$4x - y = -2$
