Answer:
b = -20
Step-by-step explanation:
Let's start by finding the slope of the line.
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Origin: (0, 0)
We can use (0, 0) and (3, 5) to find the slope:
[tex]Slope=\frac{5-0}{3-0}=\frac{5}{3}[/tex]
Then, we can plug this into the equation for slope to find the value of b (the slope has to be the same, since they're on the same line)
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{5}{3}=\frac{b-5}{-12-3}\\\frac{5}{3}=\frac{b-5}{-15}\\\text{Multiply both sides by -15}\\\frac{5}{3}(-15)=b-5\\\frac{-75}{3}=b-5\\-25=b-5\\\text{Add 5 to both sides}\\b=-20[/tex]
