Question

Given the line is parallel to the line y=-4x+5 and through the point (-2,8).

Answer 1

Given that a line is parallel to another line (y = -4x + 5), and it passes through the point (-2, 8), the equation of the parallel line is derived as;

`\begin{gathered} y=mx+b \\ (x,y)=(-2,8) \\ 8=-4(-2)+b \\ 8=8+b \\ 8-8=b \\ b=0 \end{gathered}`

Note that when two lines are parallel, their slopes are equal. Therefore, having calculated the value of b as 0, and given the slope as -4 (coefficient of x), the equation of the parallel line is;

`\begin{gathered} y=mx+b \\ y=-4x+0 \\ y=-4x \end{gathered}`

The line that is parallel to y = -4x + 5 and passes through the point (-2, 8) is;

y = -4x