Question

What is the slope-intercept form(-2,-1),(-4,-3)

Answer 1

To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}$

So, in this case, we have:

$\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-4,-3) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-(-1)}{-4-(-2)} \\ m=\frac{-3+1}{-4+2} \\ m=\frac{-2}{-2} \\ m=1 \end{gathered}$

Now, we can use the point-slope formula, and we solve for y:

$y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula}$$\begin{gathered} y-(-1)=1(x-(-2)) \\ y+1=x+2 \\ \text{ Subtract 1 from both sides of the equation} \\ y+1-1=x+2-1 \\ y=x+1 \end{gathered}$

Therefore, the equation of the line that passes through the points (-2, -1) and (-4, -3) in its slope-intercept form is:

$\boldsymbol{y=x+1}$