What is the equation in slope-intercept form of the line that crosses the x-axis at 21 and is perpendicular to the line represented by y = 7/2x-13

Question

asked Dec 11, 2022 147k views

1 Answer

Sambo · Answer 1 · 2022-12-14T22:45:50+0000

Given:

A line is perpendicular to the line
y=(7)/(2)x-13 .

The line passes through the x-axis at 21.

To find:

The equation of the line in slope intercept form.

Solution:

The slope intercept form of a line is:

y=mx+b

Where, m is the slope and b is the y-intercept.

The given line is:

y=(7)/(2)x-13

So, the slope of this line is
(7)/(2) .

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

Let m be the slope of required line. Then the slope of the required line is:

m* (7)/(2)=-1

m=-(2)/(7)

The line passes through the x-axis at 21. It means the line passes through the point (21,0). So, the equation of the line is:

y-y_1=m(x-x_1)

y-0=-(2)/(7)(x-21)

y=-(2)/(7)(x)-(2)/(7)(-21)

y=-(2)/(7)x+6

Therefore, the equation of the required line is
.