Answer:
a = -1
Step-by-step explanation:
If the gradient of the line joining (4, a) and (7, 5) is 2 it means that
m = 2
so we use the gradient formula to calculate the value of a because both these points line on the same line so we can use these two points to calculate our gradient and then equate it like this,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-a}{7-4}\\\\m=\frac{5-a}{3}\\[/tex]
now since the gradient is 2 we replace m with the number 2
it becomes like this ,
[tex]m=\frac{5-a}{3}\\\\2=\frac{5-a}{3}\\\\3(2)=5-a\\6=5-a\\6+a=5\\a=5-6\\a=-1\\[/tex]
