Question

Solve the problem below: Write an equation of the line that is parallel to the given line y = 2x + 3 and passes through the point (-4, 1).

Answer 1

Lines are parallel if they have the same slope. In the given equation, y = 2x + 3, the slope is 2. Hence, any line parallel to this line must have a slope of 2 as well.

If this other line passes through the point (-4, 1) with a slope of 2, we can get the equation using slope-point form of the equation. The formula is:

`y-y_1=m(x-x_1)`

where m = slope and (x₁, y₁) are the coordinates of the point on that line.

Since we already have the slope and the coordinate of the point on that line, let's plug them in to the formula above.

`y-1=2(x-(-4))`

Solve for y.

`\begin{gathered} y-1=2(x+4) \\ y-1=2x+8 \\ y=2x+8+1 \\ y=2x+9 \end{gathered}`

Hence, the equation of the line parallel to y = 2x + 3 and passes through the point (-4, 1) is y = 2x + 9.