Question

Write an equation of the line that passes through the given point P(-2,4), and is parallel to the line y=4x-4

Answer 1

y = 4x + 12

Step-by-step explanation:

The slope-intercept form of the equation of a line is generally given as;

`y=mx+b`

where m = the slope of the line

b = y-intercept of the line

Given the below equation of the line in the question;

`y=4x-4`

We can see that the slope(m) of the line is 4.

Note that parallel lines always have the same slope.

Therefore any line that is parallel to the given line will have a slope of 4 too.

Let's go ahead and use the point-slope form of the equation of a line to write the required equation of the parallel line with slope(m) = 4 and point coordinates x1 = -2 and y1 = 4;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-4=4\lbrack(x-(-2)\rbrack \\ y-4=4(x+2) \\ y-4=4x+8 \\ y=4x+8+4 \\ y=4x+12 \end{gathered}`