Answer:
The equation of the line:
- [tex]y\:=\:\frac{-3}{2}x\:+\frac{7}{2}[/tex]
Step-by-step explanation:
We know the slope-intercept of line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given the points
Finding the slope between two points (3, -1) and (-1, 5)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(-1,\:5\right)[/tex]
[tex]m=\frac{5-\left(-1\right)}{-1-3}[/tex]
[tex]m=-\frac{3}{2}[/tex]
substituting m = -3/2 and the point (3, -1) in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]-1=-\frac{3}{2}\left(3\right)+b[/tex]
[tex]-\frac{9}{2}+b=-1[/tex]
Add 9/2 to both sides
[tex]-\frac{9}{2}+b+\frac{9}{2}=-1+\frac{9}{2}[/tex]
[tex]b=\frac{7}{2}[/tex]
now substituting b = 7/2 and m = -3/2 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-3}{2}x\:+\frac{7}{2}[/tex]
Therefore, the equation of the line:
- [tex]y\:=\:\frac{-3}{2}x\:+\frac{7}{2}[/tex]
