Question

Fine the line that is parellel toY= 2x +4 and passes through(-3,5)

Answer 1

To determine if a line is parallel to another, we need to find the slope of the given linear equation, since the parallel line is going to have the same slope.

The slope of a line m can be determined by first puting the linear equation into the slope-intercept form, which is

y = mx + b.

Given the equation as

y = 2x + 4, the slope is 2

However to solve for b, we can start by substituting for the values of y and x which are given as the coordinates of the point through which the line passes.

The given equation is;

$\begin{gathered} y=mx+b \\ y=2x+b \\ \text{Substitute for the values of x and y} \\ 5=2(-3)+b \\ 5=-6+b \\ 11=b \\ \text{Having calculated b as 11, we now have the parallel equation as;} \\ y=2x+11 \end{gathered}$

The line parallel to y = 2x + 4 is derived as

y = 2x + 11