Answer:
The equation of the line fully simplified slope-intercept form:
- [tex]y\:=\:\frac{5}{3}x-5[/tex]
Step-by-step explanation:
We know the slope-intercept form of the line equation is
[tex]y = mx + b[/tex]
where m is the slope and b is the y-intercept
Given the points on the line
Finding the slope between the points (0, -5) and (3, 0)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)[/tex]
[tex]m=\frac{0-\left(-5\right)}{3-0}[/tex]
[tex]m=\frac{5}{3}[/tex]
We know the y-intercept can be determined by setting x = 0 and solving for y.
From the graph, it is clear that
at x = 0, y = -5
Thus, the y-intercept = b = -5
now substituting b = -5 and m = 5/3 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{5}{3}x+\left(-5\right)[/tex]
[tex]y\:=\:\frac{5}{3}x-5[/tex]
Thus, the equation of the line fully simplified slope-intercept form:
- [tex]y\:=\:\frac{5}{3}x-5[/tex]
