Question

Write the equation of the line fully simplified slope-intercept form.

Answer 1

The equation of the line fully simplified slope-intercept form:

• 
  `y\:=\:(5)/(3)x-5`

Explanation:

We know the slope-intercept form of the line equation is

`y = mx + b`

where m is the slope and b is the y-intercept

Given the points on the line

• (0, -5)

• (3, 0)

Finding the slope between the points (0, -5) and (3, 0)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)`

`m=(0-\left(-5\right))/(3-0)`

`m=(5)/(3)`

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`

`y\:=\:(5)/(3)x+\left(-5\right)`

`y\:=\:(5)/(3)x-5`

Thus, the equation of the line fully simplified slope-intercept form:

• 
  `y\:=\:(5)/(3)x-5`