Question

3. Find the equation ofthe line:through (-2.2). parallel to y=-3x

Answer 1

The given equation is

`y=-3x`

Remember that the slope is the coefficient of x. So, the slope of the given line is -3.

According to the problem, the new line is parallel to the given equation, which means it has the same slope. So, the slope of the new parallel line is -3.

Then, we use the point-slope formula to find the equation.

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

Let's replace the slope -3 and the point (-2, 2).

`\begin{gathered} y-2=-3(x-(-2)) \\ y-2=-3x-6 \\ y=-3x-6+2 \\ y=-3x-4 \end{gathered}`

Therefore, the equation of the new line is y = -3x - 4.