Question

Find the equation of the line through (1,-5) and (7,1) write the equation in slope intercept form.

Answer 1

The points are (1, - 5) and (7, 1).

Slope - intercept form : y = mx + b.

Line equation formula : y - y₁ = m(x - x₁).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substitute the values of (x₁, y₁) = (1, - 5), (x₂, y₂) = (7, 1) in (m) = (y₂ - y₁)/(x₂ - x₁).

= (1 + 5)/(7 - 1)

= (6)/(6)

m = 1.

Substitute the values of (x₁, y₁) = (1, - 5) and m = 1 in Line equation formula.

y + 5 = 1(x - 1)

y + 5 = x - 1

Subtract 5 from each side.

y  = x - 1 - 5

y = x - 6.

The slope - intercept form of the line is y = x - 6.

Answer 2

Slope - intercept form line equation is y = mx + b where m is slope and b is y-intercept.

First find the slope using slope formula (m) = (y₂ - y₁)/(x₂ - x₁)

= (1 + 5)/(7 - 1)

= (6)/(6) = 1

 

The line equation is y  = x+ b

Find y-intercept value by substituting any point on the line say (7, 1)

1 = 1 * 7 + b

b = 1 - 7 = - 6

 

The line equation is y = x - 6