write an equation of the line that passes through each pair of points. find the slope and y-intercept.

Question

1. (1,1) (7,4)
2. (5,7) (0,6)
3. (-5/4,1) (-1/4,3/4)
how do you find the y - intercept ?

Answer 1

1) The points are (1, 1), (7, 4)

Slope - intercept form : y = mx + b.

Line equation formula : y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

Substitute the values of (x₁, y₁) = (1, 1), (x₂, y₂) = (7, 4) in Line equation formula.

y - 1 = [(4 - 1)/(7 - 1)](x - 1)

y - 1 = [3/6](x - 1)

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

Add 1 to each side.

y  = (1/2)x - 1/2 + 1

y = (1/2)x + 1/2.

Compare the above equation with Slope - intercept form : y = mx + b.

Slope(m) = 1/2 and y - intercept(b) = 1/2.

2) The points are (5, 7), (0, 6)

Slope - intercept form : y = mx + b.

Line equation formula : y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

Substitute the values of (x₁, y₁) = (5, 7), (x₂, y₂) = (0, 6) in Line equation formula.

y - 7 = [(6 - 7)/(0 - 5)](x - 5)

y - 7 = [- 1/- 5](x - 5)

y - 7 = (1/5)x - 1

Add 7 to each side.

y  = (1/5)x - 1 + 7

y = (1/5)x + 6

Compare the above equation with Slope - intercept form : y = mx + b.

Slope(m) = 1/5 and y - intercept(b) = 6.

3) The points are (- 5/4, 1), (- 1/4, 3/4)

Slope - intercept form : y = mx + b.

Line equation formula : y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

Substitute the values of (x₁, y₁) = (- 5/4, 1), (x₂, y₂) = (- 1/4, 3/4) in Line equation formula.

y - 1 = [(3/4) - (1)/[( - 1/4) + (5/4)]](x + (5/4))

y - 1 = (- 1/4)(x + (5/4))

Add 1 to each side.

y  = (- 1/4)x - (5/16) + 1

y = (- 1/4)x +11/16.

Compare the above equation with Slope - intercept form : y = mx + b.

Slope(m) = - 1/4 and y - intercept(b) = 11/16.