Question

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

Answer 1

Answer:

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

• $y\:=\:\frac{5}{3}x-5$

Step-by-step 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)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{0-\left(-5\right)}{3-0}$

$m=\frac{5}{3}$

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

$y = mx+b$

$y\:=\:\frac{5}{3}x+\left(-5\right)$

$y\:=\:\frac{5}{3}x-5$

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

• $y\:=\:\frac{5}{3}x-5$