Answer:
- The equation of the line is:
[tex]y=\frac{1}{2}x-2[/tex]
Step-by-step explanation:
Given the points
Finding the slope between two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-2\right)[/tex]
[tex]m=\frac{1}{2}[/tex]
We know that the y-intercept can be obtained by setting the value x=0 and solving for y.
From the graph, it is clear that at x=0, the value of y = -2
Thus, the y-intercept (b) = -2
We 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=1/2 and y-interept (b) = -2 in the slope-intercept form of the line equation
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{2}x+\left(-2\right)[/tex]
[tex]y=\frac{1}{2}x-2[/tex]
Thus, the equation of the line is:
[tex]y=\frac{1}{2}x-2[/tex]
