Question

Write an equation in point-slope form for the line that passes through each point with the given slope.

$\left(-2,-1\right),m=-3$

Short answer

The equation of the straight line for the given condition is $\mathit{y}\mathbf{=}\mathbf{-}\mathbf{3}\mathit{x}\mathbf{-}\mathbf{7}$.

Step-by-step solution

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$is the slope of the straight line and $c$is the $y$-intercept of the equation.

Step 2. State the equation of a line slope-point form.

The standard form of slope and point form of the straight line is$y-y_1=m\left(x-x_1\right)$

Here $m$is the slope of the straight line and is the point from which the straight line passes.

localid="1647421972969" $$\begin{gathered} \left(x_1,y_1\right)=\left(-2,-1\right) \\ m=-3 \end{gathered}$$

Step 3. Substitute the values to get the required equation.

Substitute the above values in the equation$y-y_1=m\left(x-x_1\right)$

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-\left(-1\right)=-3\left(x-\left(-2\right)\right) \\ y+1=-3x-6 \\ y=-3x-7 \end{gathered}$$

The equation of the straight line is $y=-3x-7$.