Lines A and B are perpendicular and have the same x-intercept. The equation of line A
is x + 2y - 4 = 0 . Determine the y-intercept of line B.
A.-8
B.-2
C. 4
D. 8
This is the work that I did:
x + 2y - 4 = 0
+4 +4
x+2y = 4
-x -x
2y = -x+4
divide both sides by 2
and I got -1/2x+2
I thought that the answer would be -2 maybe but its -8. How is it -8?
x + 2y - 4 = 0
x + 2y = 4
to find x-intercept, y = 0
x + 2(0) = 4
x = 4
x-intercept = (4.0)
slope intercept form (which you got right above) y = mx + b
for Line A is y = -1/2 x + 2
slope m = -1/2
If two lines are perpendicular, the slope of one is the negative reciprocal of the slope of the other.
Slope of Line B = ?
Line B through point (4,0)(line A and B have the same x-intercept)
To write equation of Line B
plug slope m in y = mx + b, and use point (4,0) to solve for b, which is the y-intercept.
To determine the y-intercept of line B, you need to find the equation of line B based on the given information.
Since lines A and B are perpendicular, their slopes are negative reciprocals of each other. The equation of line A is x + 2y - 4 = 0, which can be rewritten as 2y = -x + 4 or y = -1/2 * x + 2.
To find the slope of line A, notice that the coefficient of x is -1/2. The slope of line B would be the negative reciprocal of the slope of line A, which is 2.
Now that we know the slope of line B is 2 and that it has the same x-intercept as line A, we can use the point-slope form of a linear equation to find the equation of line B.
Using the x-intercept, we have a point with coordinates (4, 0) since the x-intercept is the value of x when y = 0. Plugging in this point and the slope into the point-slope form (y - y1 = m(x - x1)), the equation of line B becomes:
y - 0 = 2(x - 4)
y = 2x - 8
So, the equation of line B is y = 2x - 8. By comparing it to the general form of a linear equation (y = mx + b), we can see that the y-intercept of line B is -8.
Therefore, the correct answer is option A: -8.