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)
