Question

The equation of line EF is y = x + 6. Write an equation of a line parallel to line EF in slope-intercept form that contains point (0, −2).

Answer 1

in order to be parallel, they must have the same slope but different y-intercept. in this case the slope is m=1. since the line must go through (0, -2) plug that into the equation and solve for the b, the y-intercept of the line you want:

\(\large y=mx+b \rightarrow -2=1 \cdot (0) + b \)

once you have the value for b, replace that into the equation to get your answer.

Answer 2

so... as @ByteMe said, the slope is 1 for y = x+6 notice it \(\bf y = {\color{red}{ 1}}x+6\)

so you want the equation of a line with the same slope of 1, and that passes through (0,-2) so \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 0}}\quad ,&{\color{blue}{ -2}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 1
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form} \)