a)The equation of the graph is y = 1/2x + 11/3
b) Distance covered after 6 mins is 8.4 miles
How to derive line equation
Let's consider points (1,4) and (5,6),
Using the formula
y - y₁ = m(x - x₁)
where
(x₁, y₁) is a point on the line, and m is the slope.
z Find the slope m
m = y₂ - y₁/x₂ - x₁
Substituting the coordinates (1,4) and (5,6)
m = 6 - 4/5 - 1
= 2/4 = 1/2
Choose one of the points, let's use (1,4), and substitute into the point-slope form:
y = mx + b
m = 1/2
b = 3 2/3 = 11/3
So, the equation of the line passing through the points (1,4) and (5,6) is y = 1/2x + 11/3
b) area under the graph = distance covered
A = area of triangle
= 1/2*7*2.4 = 8.4 miles
Complete question