Question

Find the equation of the line parallel to 7y+2x-10=0 that passes through the point (2,2)

Answer 1

Parallel lines have the same slope.

We have the general form of line. Transform to the slope-intercept form:

$y=mx+b$

m - slope, b - y-intercept

$7y+2x-10=0$      subtract 2x from both sides

$7y-10=-2x$       add 10 to both sides

$7y=-2x+10$       divide both sides by 7

$y=-\dfrac{2}{7}x+\dfrac{10}{7}\to m=-\dfrac{2}{7}$

Therefore we have: $y=-\dfrac{2}{7}x+b$.

The line passes through the point (2, 2). Substitute the coordinates of the point to the equation of a line:

$2=-\dfrac{2}{7}(2)+b$

$2=-\dfrac{4}{7}+b$      add $\dfrac{4}{7}$ to both sides

$2\dfrac{4}{7}=b$

$y=-\dfrac{2}{7}x+2\dfrac{4}{7}$

$y=-\dfrac{2}{7}x+\dfrac{18}{7}$     multiply both sides by 7

$7y=-2x+18$       subtract 7y from both sides

$0=-2x-7y+18$      change the signs

$2x+7y-18=0$

Answer:

$y=-\dfrac{2}{7}x+\dfrac{18}{7}$  slope-intercept form

$2x+7y-18=0$   general form