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