Question

do you think you might be able to help me with this today

Answer 1

To solve the exercise you can first take two points through which the line passes, find the slope of the line and then use the point-slope formula.

So if you take the points

$\begin{gathered} (x_1,y_1)=(-3,-2) \\ (x_2,y_2)=(3,4) \end{gathered}$

you can find the slope of the line using the formula

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}$$\begin{gathered} m=\frac{4-(-2)}{3-(-3)} \\ m=\frac{4+2}{3+3} \\ m=\frac{6}{6} \\ m=1 \end{gathered}$

Finally, using the point-slope formula, you have

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)_{}=1(x-(-3)) \\ y+2=1(x+3) \\ y+2=x+3 \\ \text{ Subtract 2 from both sides of the equation} \\ y+2-2=x+3-2 \\ y=x+1 \end{gathered}$

Therefore, the equation of the line in its slope-intercept form is

$\begin{gathered} y=x+1 \\ \text{ Where} \\ \text{the slope is 1 and} \\ y-\text{intercept es 1} \end{gathered}$