Answer:
[tex]y=-x-2[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given line:
[tex]y=-x+6[/tex]
Therefore, the slope of the given line is -1.
Parallel lines have the same slope. Therefore, the slope of the line that is parallel to the given line is -1.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and the given point (0, -2) into the point-slope formula:
[tex]\implies y-(-2)=-1(x-0)[/tex]
[tex]\implies y+2=-x[/tex]
[tex]\implies y+2-2=-x-2[/tex]
[tex]\implies y=-x-2[/tex]
Therefore, the equation of the line in slope-intercept form that passes through point (0, -2) and is parallel to the line y = -x + 6 is:
