Answer:
The slope of the graph will be:
From the attached graph, it is clear that
- the y-intercept is: (5, 0) ∵ to find the y-intercept, set x=0
- the x-intercept is: (0, -4) ∵ to find the x-intercept, set y=0
Step-by-step explanation:
Given the two points on the line
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:-4\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)[/tex]
[tex]m=\frac{0-\left(-4\right)}{3-0}[/tex]
[tex]m=\frac{4}{3}[/tex]
Hence, the slope of the graph will be:
[tex]m=\frac{4}{3}[/tex]
We can also find the equation of the line using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 4/3 and the point (0, -4)
[tex]y-\left(-4\right)=\frac{4}{3}\left(x-0\right)[/tex]
[tex]y+4=\frac{4}{3}\left(x-0\right)[/tex]
[tex]y+4=\frac{4}{3}x[/tex]
[tex]y=\frac{4}{3}x-4[/tex]
Therefore, the equation of the line will be:
[tex]y=\frac{4}{3}x-4[/tex]
The graph of the equation line is also attached below.
From the graph, it is clear that
- the y-intercept is: (5, 0) ∵ to find the y-intercept, set x=0
- the x-intercept is: (0, -4) ∵ to find the x-intercept, set y=0
