The value of m=2 and the value of c=-8.
What is the equation of a straight line?
The equation of a straight line y=mx+c where m is the slope of the straight line and c is the distance the straight line is away from the origin along the y-axis.
How to solve this?
The given line is y=2x+4 which cuts the x-axis at the point A= (-2,0).
To determine this,
let (x,y) satisfy the straight line and it is on the x-axis.
Then, y=0 and y=2x+4 are the two equations that (x,y) must satisfy.
So, putting y=0 in y=2x+4 yields x=-2.
Hence, A=(-2,0) is the point at which the line y=2x+4 cuts the x-axis.
Now, point B is 6 units away from A along the x-axis.
This means that B=(-2+6,0)=(4,0).
Now, the new line y=mx+c passes through point B=(4,0) which means it must satisfy the line.
Moreover, in the new line m=2 because the line is parallel to y=2x+4 and parallel lines have the same slope.
And hence,
0=2(4)+c
⇒c=-8.
Hence, the required straight line is y=2x-8, the value of m=2, and the value of c=-8.
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