Question

What is the y-intercept of the equation of the line that is perpendicular to the line y =3/5 x 10 and passes through the point (15, –5)?the equation of the line in slope-intercept form is y =-5/3 x

Answer 1

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Answer 2

Answer:

The y-intercept of the equation of the line is 20.

Step-by-step explanation:

The equation of given line is

$y=\frac{3}{5}x+10$

It is a slope intercept form of a line (y=mx+b), where m is slope and b is y-intercept.

The slope of the line is

$m_1=\frac{3}{5}$

The product of slopes of two perpendicular lines is -1.

$m_1\times m_2=-1$

$\frac{3}{5}\times m_2=-1$

$m_2=-\frac{5}{3}$

The slope of required line is $-\frac{5}{3}$ and it is passing through the point (15,-5).

The point slope form of a line is

$y-y_1=m(x-x_1)$

$y-(-5)=-\frac{5}{3}(x-15)$

$y+5=-\frac{5}{3}(x)+25$

$y=-\frac{5}{3}(x)+20$

The slope intercept form of required line is $y=-\frac{5}{3}(x)+20$.

Therefore y-intercept of line is 20.