Question

All the points in the picture are on the same line. Find the slope of the line. Explain or show your reasoning. Write an equation for the line. Find the values for a and b explain or show your reasoning

Answer 1

The slope of the line is 2.

The equation of the line is y = 2x - 1.

The value of a is 4.

The value of b is 5.

How to calculated the slope of the line?

The slope of the line is calculated as follows;

m = Δ y / Δ x

m = (y₂ - y₁) / (x₂ - x₁)

Using the following points;

(6, 11), and (1, 1)

m = (11 - 1) / ( 6 - 1)

m = 10 / 5

m = 2

The equation of the line becomes;

(y - y₁) /(x - x₁) = m

(y - 1) / (x - 1) = 2

y - 1 = 2(x - 1)

y - 1 = 2x - 2

y = 2x - 1

The value of a is calculated as;

(a, 7)

y = 2x - 1

7 = 2(a) - 1

2a = 8

a = 8 / 2

a = 4

The value of b is calculated as;

(3, b)

y = 2x - 1

b = 2(3) - 1

b = 6 - 1

b = 5