Answer:
a = 9
Step-by-step explanation:
• Parallel lines have equal gradients
Calculate the gradient m of the line joining the 2 points, then equate to the given gradient of 3.
calculate the gradient m, using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = A (1, 3 ) and (x₂, y₂ ) = B (3, a )
substitute these values into the formula for m
m = [tex]\frac{a-3}{3-1}[/tex] = [tex]\frac{a-3}{2}[/tex]
Now, equate this expression for m to m = 3
[tex]\frac{a-3}{2}[/tex] = 3 ( multiply both sides by 2 )
a - 3 = 6 ( add 3 to both sides )
a = 9
