Question

Give the slope-intercept form of the equation of the line that is perpendicular to –7x + 5y = 12 and contains P(–7, 4).

Answer 1

y = - $\frac{5}{7}$ x - 1

the equation of a line in slope-intercept form is

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

rearrange - 7x + 5y = 12 into this form

add 7x to both sides

5y = 7x + 12 ( divide all terms by 5 )

y = $\frac{7}{5}$ x + $\frac{12}{5}$ ← in slope- intercept form

with slope m = $\frac{7}{5}$

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

perpendicular slope = - $\frac{1}{m}$ = - $\frac{5}{7}$

The partial equation of the perpendicular line is

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

to find c substitute (- 7, 4 ) into the partial equation

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = - $\frac{5}{7}$ x - 1 ← in slope- intercept form