Question

Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form

Answer 1

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=(y_2-y_1)/(x_2-x_1) \\ m=(-1-0)/(0-(-2)) \\ m=-(1)/(2) \end{gathered}`

Now that we have both m and b. Substitute these values to the slope intercept form

`\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-(1)/(2)x-1 \end{gathered}`