(-3,6); 7x = 3y + 2
Write an equation of the line containing the given point
and parallel to the given line. Express in y = mx + b form.
As always, start by finding the slope of the given line.
7x = 3y + 2
3y = 7x - 2
y = 7/3 x - 2/3
To be parallel to the given line, the line we want will
have the same slope, 7/3.
We find the y-intercept of the new line by solving
y = mx + b for b: b = y - mx. Then, we plug in the
x and y values of the point we were given.
b = 6 - (7/3 * -3)
b = 6 - (-7)
b = 6 + 7
b = 13
The equation we want is y = 7/3 x + 13