Lines y + 2 = 7 and y − 4x = – 3 intersect on a standard
(x, y) coordinate plane. What is the x-coordinate of the
point where the two lines intersect?
F.
2
G.
3
H.
4
J.
5
K.
6
To find the x-coordinate of the point where the two lines intersect, we can set the two equations equal to each other and solve for x.
First, let's rewrite the equations in slope-intercept form (y = mx + b) to make it easier to compare and set them equal to each other:
y + 2 = 7 can be rewritten as y = -2x + 5
y - 4x = -3 can be rewritten as y = 4x - 3
Now we can set these two equations equal to each other and solve for x:
-2x + 5 = 4x - 3
Adding 2x to both sides and subtracting 5 from both sides, we get:
8 = 6x
Dividing by 6, we find:
x = 8/6
Simplifying the fraction, we get:
x = 4/3
Therefore, the x-coordinate of the point where the two lines intersect is 4/3.
The answer is H. 4.