Question

write a slope-intercept equation for a line passing through the point (5,-4) that is perpendicular to the line 5x+6y=7

Answer 1

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 5x + 6y = 7 into this form

subtract 5x from both sides

6y = - 5x + 7 ( divide all terms by 6 )

y = - $\frac{5}{6}$ x + $\frac{7}{6}$ ← in slope-intercept form

with slope m = - $\frac{5}{6}$

given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$, hence

$m_{perpendicular}$ = - 1 / - $\frac{5}{6}$ = $\frac{6}{5}$

y = $\frac{6}{5}$ x + c ← is the partial equation

to find c substitute (5, - 4 ) into the partial equation

- 4 = 6 + c ⇒ c = - 4 - 6 = - 10

y = $\frac{6}{5}$ x - 10 ← equation in slope-intercept form