Answer:
[tex]y=-3x-4[/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 the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (−3, 5) and (2, -10)
[tex]m=\frac{-10-5}{2-(-3)}\\m=\frac{-10-5}{2+3}\\m=\frac{-15}{5}\\m=-3[/tex]
Therefore, the slope is -3. Plug -3 into [tex]y=mx+b[/tex] as m:
[tex]y=-3x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-3x+b[/tex]
Plug one of the given points, (−3, 5) or (2, -10) into the equation and isolate b
[tex]5=-3(-3)+b\\5=9+b[/tex]
Subtract 9 from both sides
[tex]5-9=9+b-9\\-4=b[/tex]
Therefore, the y-intercept is -4. Plug -4 into [tex]y=-3x+b[/tex] as b:
[tex]y=-3x-4[/tex]
I hope this helps!
