Question

Find an equation of the line parallel to −5x+7y=3 that passes through the point (9,−4). If possible, write the equation in slope-intercept form.

Answer 1

From the original equation we have:

$-5x+7y=3$$7y=5x+3$$y=\frac{5}{7}x+\frac{3}{7}$

The slope of this line is 5/7 and for the new equation to be parallel to the original must have the same slope, and using the point-slope formula we have:

$y-(-4)=\frac{5}{7}(x-9)$$y+4=\frac{5}{7}x-\frac{45}{7}$$y=\frac{5}{7}x-\frac{45}{7}-4$$y=\frac{5}{7}x-\frac{73}{7}$