Answer:
The equation of the line fully simplified slope-intercept form:
Step-by-step explanation:
We know the slope-intercept form of the line equation is
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
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)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(0,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%280%2C%5C%3A-5%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%283%2C%5C%3A0%5Cright%29)
![m=\frac{0-\left(-5\right)}{3-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B0-%5Cleft%28-5%5Cright%29%7D%7B3-0%7D)
![m=\frac{5}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B3%7D)
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
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
![y\:=\:\frac{5}{3}x+\left(-5\right)](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B5%7D%7B3%7Dx%2B%5Cleft%28-5%5Cright%29)
![y\:=\:\frac{5}{3}x-5](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B5%7D%7B3%7Dx-5)
Thus, the equation of the line fully simplified slope-intercept form: