Answer:
a = -4
Step-by-step explanation:
The equation for slope is:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can substitute the given values into the equation:
[tex]3=\frac{2a+1-5}{-5-(a+3)}\\3=\frac{2a-4}{-5-a-3}\\3=\frac{2a-4}{-8-a}[/tex]
Multiply both sides by -8-a:
[tex]3(-8-a)=2a-4\\\\\text{distribute the 3 to each term in the parentheses}\\\\-24-3a=2a-4\\\\\text{add 4 to both sides}\\\\-20-3a=2a\\\\\text{add 3a to both sides}\\\\5a=-20\\\\\text{divide both sides by 5}\\a=-4[/tex]
