the value of x if: y=4x+7

Question

value of k ,if the equation of a line is defined by (3-2k)x+y=12 ,the line is parallel to y=4x+7

Answer 1

(3-2k)x+y=12 parallel to y=4x+7, so it must have a gradient (slope) of 4 because y=4x+7 has a gradient of 4.

y=12-(3-2k)x is another way of writing (3-2k)x+y=12.

The slope of this line is -(3-2k) which must be equal to the slope of the other line (=4).

-(3-2k)=4, -4=3-2k, 2k=7, k=7/2 (can be written 3½). And the equation of the line becomes y=4x+12 after substituting for k.