Answer:
The y-intercept would be:
[tex]b=\frac{53}{28}[/tex]
Step-by-step explanation:
Given the ordered pairs
(-11, 7)
(17, -6)
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-11,\:7\right),\:\left(x_2,\:y_2\right)=\left(17,\:-6\right)[/tex]
[tex]m=\frac{-6-7}{17-\left(-11\right)}[/tex]
[tex]m=-\frac{13}{28}[/tex]
Slope-intercept form to find the y-intercept
[tex]\mathbf{y=mx+b}[/tex]
Here:
m = slop
b = y-intercept
so
Putting [tex]m=-\frac{13}{28}[/tex] and any point, let say (-11, 7), in the Slope-intercept form find the y-intercept
[tex]\mathbf{y=mx+b}[/tex]
[tex]7=\left(-\frac{13}{28}\right)\left(-11\right)+b[/tex]
[tex]\left(-\frac{13}{28}\right)\left(-11\right)+b=7[/tex] ∵ switch sides
[tex]\mathrm{Subtract\:}\left(-\frac{13}{28}\right)\left(-11\right)\mathrm{\:from\:both\:sides}[/tex]
[tex]\left(-\frac{13}{28}\right)\left(-11\right)+b-\left(-\frac{13}{28}\right)\left(-11\right)=7-\left(-\frac{13}{28}\right)\left(-11\right)[/tex]
[tex]b=\frac{53}{28}[/tex] ∵ [tex]7-\left(-\frac{13}{28}\right)\left(-11\right):\quad \frac{53}{28}[/tex]
Therefore, the y-intercept would be:
