Answer:
[tex]y=\displaystyle\frac{3}{4} x+\displaystyle \frac{1}{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 (the value of y when x=0).
First, we must find the slope (m).
[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Two points that are highlighted for us on the graph are (-3,-2) and (5,4). Plug these into the equation:
[tex]m=\displaystyle\frac{4-(-2)}{5-(-3)}\\\\m=\displaystyle\frac{4+2}{5+3}\\\\m=\displaystyle\frac{6}{8}\\\\m=\frac{3}{4}[/tex]
Therefore, the slope of the line is 3/4. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle\frac{3}{4} x+b[/tex]
Now, to find the y-intercept (b), our first resort would be to find it on the graph. However, on the graph, it appears ambiguous. So, we must solve it algebraically.
[tex]y=\displaystyle\frac{3}{4} x+b[/tex]
Plug in the point (5,4) and solve for b:
[tex]4=\displaystyle\frac{3}{4} (5)+b\\\\4=\displaystyle\frac{15}{4}+b\\\\b=4-\frac{15}{4} \\\\b=\frac{1}{4}[/tex]
Therefore, the y-intercept is [tex]\displaystyle \frac{1}{4}[/tex]. Plug this back into [tex]y=\displaystyle\frac{3}{4} x+b[/tex]:
[tex]y=\displaystyle\frac{3}{4} x+\displaystyle \frac{1}{4}[/tex]
I hope this helps!
