Question

Theequationforlinegcanbewrittenas y = –9 4 x − 1 . Line h , whichisperpendiculartoline g , includesthepoint (10, 4) . What istheequationofline h ? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Answer 1

Answer:

y-4 = 4/9(x-10)

Step-by-step explanation:

Given the equation of the line g to be y = -9/4 x - 1.

To find the equation of a line h perpendicular to this line, the following steps must be taken;

First find the slope of the known line g

The standard equation of a line is y = mx+c where

m is the slope

c is the intercept

Comparing this equation with the given equation y = -9/4 x -1, it can be seen that the slope of the line g is -9/4

Next is to find the slope of the line h

Since the line g is perpendicular to h, then the product of their slope will be -1 i.e mh*mg = -1

mh = -1.mg

mh = -1/(-9/4)

mh = -1*-4/9

mh = 4/9

Hence the slope of the line h is 4/9

Find the intercept of line h

To get this, you will substitute the slope m and the point into the equation y = mx+c

m = 4/9

(x,y) = (10,4)

4 = 4/9(10) + c

4 = 40/9 + c

c = 4-40/9

c = (36-40)/9

c = -4/9

Hence the intercept of the line h is -4/9

Finally, find the equation of the line h in slope-intercept form

The slope-intercept form of a line is expressed as y = mx+c

y-y0 = m(x-x0)

Given

m = -4/9

x0 = 10

y0 = 4

Substitute:

y-4 = 4/9(x-10)

Hence the equation in slope-intercept form is y-4 = 4/9(x-10)