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Artist 52 [7]
3 years ago
14

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

Mathematics
1 answer:
hichkok12 [17]3 years ago
8 0

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


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