Answer:
C) 4
Step-by-step explanation:
Hi there!
We are given the line y=4/3x+1
We want to find the y intercept of the line perpendicular to that line, that also passes through the point (4,1)
Perpendicular lines have slopes that have a product of -1
We'll first find the slope of y=4/3x+1
The equation is written in slope-intercept form (y=mx+b), where m is the slope and b is the y intercept
4/3 is in the place of where m (the slope) is, so the slope of the line is 4/3
Now to find the slope perpendicular to it, use this formula:
4/3m=-1
Multiply both sides by 3/4
m=-3/4
The slope of the line perpendicular to y=4/3x+1 is -3/4
We can write the equation of the new line in slope-intercept form as well; start by substituting -3/4 as m:
y=mx+b
y=-3/4x+b
Now we need to find b (y intercept)
As the equation includes the point (4,1), we can use it to help solve for b
Substitute 4 as x and 1 as y:
1=-3/4(4)+b
Multiply
1=-3+b
Add -3 to both sides
4=b
The y intercept of the line is 4
Hence, the answer is C
Hope this helps!
