Find the equation of the line passing through the midpoint of A(1, 3) and B(-4, 5) with gradient 2

Explanation

Step 1: Find midpoint of A and B
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
= ((1 + (-4))/2, (3 + 5)/2)
= (-3/2, 8/2)
= (-1.5, 4)

Step 2: Use point-slope form
y – y₁ = m(x – x₁)
where m = 2, point = (-1.5, 4)

Step 3: Substitute
y – 4 = 2(x – (-1.5))
y – 4 = 2(x + 1.5)

Step 4: Expand
y – 4 = 2x + 3

Step 5: Rearrange to slope-intercept form
y = 2x + 3 + 4
y = 2x + 7