Answer:
[tex]y=3x-7[/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 (1, -4) and (3, 2):
[tex]\displaystyle m=\frac{2-(-4)}{3-1}\\\\\displaystyle m=\frac{2+4}{3-1}\\\\\displaystyle m=\frac{6}{2}\\\\\displaystyle m=3[/tex]
Therefore, the slope of the line is 3. Plug this into [tex]y=mx+b[/tex]:
[tex]y=3x+b[/tex]
Normally, we would now go about solving for the y-intercept and forming the possible equation for this line. However, there is only one choice option that has 3 as the slope. Therefore, the equation of the line must be [tex]y=3x-7[/tex].
I hope this helps!
