Answer:
The equation of line in slope-intercept form is:
[tex]y=2x+(-4)[/tex]
Step-by-step explanation:
Given the two points
slope between (0, -4) and (3, 2)
[tex]\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,\:2\right)[/tex]
[tex]m=\frac{2-\left(-4\right)}{3-0}[/tex]
[tex]m=2[/tex]
We know that 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=-4
Thus, the value of y-intercept (b) = -4
We also know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
substituting m=2 and b=-4 in the intercept form
[tex]y=mx+b[/tex]
[tex]y=2x+(-4)[/tex]
Thus, the equation of line in slope-intercept form is:
[tex]y=2x+(-4)[/tex]
