Given for problem 3:
We will find the equation of the line that passes through the points
[tex](1,-3),(3,1)[/tex]
The slope-intercept form is: y = m * x + b
where (m) is the slope, and (b) is the y-intercept
The slope will be calculated as follows:
[tex]\begin{gathered} slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-3)}{3-1}=\frac{4}{2}=2 \\ m=2 \end{gathered}[/tex]
So, the equation will be:
[tex]y=2x+b[/tex]
Substitute with (1, -3) and m = 2
The solve for b
[tex]\begin{gathered} -3=2\cdot1+b \\ -3=2+b \\ b=-3-2 \\ b=-5 \end{gathered}[/tex]
so, the answer will be the equation of the line is:
[tex]y=2x-5[/tex]
