Answer:
[tex]y=2x+5[/tex]
Step-by-step explanation:
Hi there!
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 given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-3,-1) and (1,7)
[tex]m=\frac{7-(-1)}{1-(-3)}\\m=\frac{7+1}{1+3}\\m=\frac{8}{4}\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in one of the given points and solve for b
[tex]7=2(1)+b\\7=2+b[/tex]
Subtract 2 from both sides to isolate b
[tex]7-2=2+b-2\\5=b[/tex]
Therefore, the y-intercept is 5. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x+5[/tex]
I hope this helps!
