Question

Write the line equation passing through (-4,-1) and parallel to y=-1/2x+1

Answer 1

`y=-(1)/(2)x-3`

Explanation:

`\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}}`

Given equation:

`y=-(1)/(2)x+1`

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation is:

`m=-(1)/(2)`

Substitute the found slope and given point (-4, -1) into the point-slope formula:

`\implies y-(-1)=-(1)/(2)(x-(-4))`

`\implies y+1=-(1)/(2)(x+4)`

`\implies y+1=-(1)/(2)x-2`

`\implies y=-(1)/(2)x-3`

Therefore, the equation of the line passing through (-4, -1) and parallel to the given equation is:

`\boxed{y=-(1)/(2)x-3}`