Answer:
[tex]y=\frac{4}{5}x-\frac{18}{5}[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
In the graph, the points (-3,-6) and (2,-2) are plotted clearly, so we can use these to help us find the slope. Plug them into the equation:
[tex]m=\frac{-6-(-2)}{-3-2}\\m=\frac{-6+2}{-3-2}\\m=\frac{-4}{-5}\\m=\frac{4}{5}[/tex]
Therefore, the slope of the line is [tex]\frac{4}{5}[/tex]. Plug this into [tex]y=mx+b[/tex] :
[tex]y=\frac{4}{5}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{4}{5}x+b[/tex]
Typically, given a graph, we could look at where exactly the line crosses the y-axis to determine b. However, because it appears ambiguous on this graph, we must solve it algebraically.
Plug in one of the given points (2,-2) and solve for b:
[tex]-2=\frac{4}{5}(2)+b\\-2=\frac{8}{5}+b[/tex]
Subtract [tex]\frac{8}{5}[/tex] from both sides to isolate b
[tex]-2-\frac{8}{5}=\frac{8}{5}+b-\frac{8}{5}\\-\frac{18}{5} =b[/tex]
Therefore, the y-intercept of the line is [tex]-\frac{18}{5}[/tex]. Plug this back into [tex]y=\frac{4}{5}x+b[/tex]:
[tex]y=\frac{4}{5}x+(-\frac{18}{5})\\y=\frac{4}{5}x-\frac{18}{5}[/tex]
I hope this helps!
