Question

Write an equation in slope-intercept form for the line that passes through (-3, 5), and is perpendicular to the graph of 5x - 6y = 9

Answer 1

Y =-6/5x+7/5 Please vote me as brainliest if you think i helped and i attached a photo with work as well :) Have a great day

Answer 2

Answer:

Equation of line in slope-intercept form:

$y=-\frac{6}{5}x+\frac{7}{5}$

Step-by-step explanation:

Equation of a line in slope-intercept form is:

y = mx + c

where m is the slope and c is the y-intercept.

Given that (-3,5) passes through the line,hence:

5 = -3m+c ------------1

Also the line is perpendicular to 5x - 6y = 9.

Slope of a line ax+by+c=0 is $\frac{-a}{b}$

Hence slope of 5x - 6y = 9 is $\frac{5}{6}$

Relation between slopes of two perpendicular lines:

$m_1\times m_2=-1$

Using above relation, m= $-\frac{6}{5}$.

Substituting m = -6/5 in equation 1, we get:

c = 5 + 3(-6/5)

$c=\frac{7}{5}$

Putting m = $-\frac{6}{5}$ and c = $\frac{7}{5}$

we get:

$y=-\frac{6}{5}x+\frac{7}{5}\\6x+5y=7$