Answer:
m = 2, c = -8.
Explanation:
The general form of a straight line equation is
y = mx + c where m = the slope and c is the y-intercept.
We are given the line
y = 2x + 4
Comparing this with the general form we see that the slope of this line = 2 and the y-intercept C is 4.
Now the given line y = mx + c is parallel to y = 2x + 4 which means that their slopes are the same so we conclude that m = 2.
Now we need to find the value of c which is the y intercept of y = mx + c.
Consider the points A and B:
A is the point where the line y = 2x + 4 intersects the x axis so y = 0 at this point , So substituting in the equation:
0 = 2x + 4
-4 = 2x
x = -2.
So the point A is (-2, 0)
B is the point where y = 2x + c cuts the x axis so here y = 0:
0 = 2x + c
2x = -c
x = -c/2.
Now we are given that the 2 intercepts are 6 units apart, so:
-c/2 - (-2) = 6
-c/2 + 2 = 6
-c/2 = 4
-c = 8
c = -8.