how do you solve this

Question

A line passes through the points (2,a) and (4a,5) with a slope of 2. Find the value of a.

Answer 1

According to the slope formula, the slope of the line that passes through points (x1,y1) and (x₂,y₂) is given by the formula:

slope=m=(y₂-y₁)/(x₂-x₁)

The slope of the given line that passes through the points (2,a) and (4a,5) with x1=2, y1=a, x2=4a,y2=5 is then:

slope=m=(5-a)/(4a-2).

But on the other hand we are also given that the slope of the line is 2.

Thus we must have that slope=(5-a)/(4a-2)=2.

Multiplying both sides of the equation by (4a-2) to clear the equation of fractions yields 5-a=2(4a-2).

Distributing the 2 on the right side of the equation gives:

5-a=8a-4

subtract 8a from both sides:

5-9a=-4

subtract 5 from both sides:

-9a=-9

divide both sides by -9:

a=-9/(-9)

a=1.