Answer:
[tex]y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}[/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.
1) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
In the graph, two points are indicated: (-5,5) and (3,3). Plug these into the equation:
[tex]m=\displaystyle \frac{3-5}{3-(-5)}\\\\m=\displaystyle \frac{3-5}{3+5}\\\\m=\displaystyle \frac{-2}{8}\\\\m=\displaystyle \frac{-1}{4}[/tex]
Therefore, the slope of the line is [tex]\displaystyle -\frac{1}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle -\frac{1}{4}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle -\frac{1}{4}x+b[/tex]
Plug in one of the points we used earlier and solve for b:
[tex]3=\displaystyle -\frac{1}{4}(3)+b\\\\3=\displaystyle -\frac{3}{4}+b\\\\3+\displaystyle \frac{3}{4}=b\\\\\frac{15}{4} =b[/tex]
Therefore, [tex]\displaystyle \frac{15}{4}[/tex] is the y-intercept. Plug this back into [tex]y=\displaystyle -\frac{1}{4}x+b[/tex]:
[tex]y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}[/tex]
I hope this helps!
