Answer:
The equation of the line is:
y = 2/3x - 3
The graph is also attached below.
Step-by-step explanation:
From the given diagram, let us take two points
(0, -3)
(4.5, 0)
Determining the slope between (0, -3) and (4.5, 0)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:-3\right),\:\left(x_2,\:y_2\right)=\left(4.5,\:0\right)[/tex]
[tex]m=\frac{0-\left(-3\right)}{4.5-0}[/tex]
[tex]m\:=\frac{3}{4.5}[/tex]
[tex]m=\frac{3}{\frac{45}{10}}[/tex]
[tex]m=\frac{3\cdot \:10}{45}[/tex]
[tex]m=\frac{2}{3}[/tex]
Therefore, the slope of the line is:
m = 2/3
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
From the given point
It is clear that at x = 0, the value of y = -3
Thus, the y-intercept b = -3
now substituting b = -3 and m = 2/3 in the slope-intercept form of the line equation
y = mx+b
y = 2/3x + (-3)
y = 2/3x - 3
Therefore, the equation of the line is:
y = 2/3x - 3
The graph is also attached below.
