In Problems i-iv,

Question

a) Find the slope of the line that passes through the given points.

b) Find the point-slope form of the equation of the line.

c) Find the slope-intercept form of the equation of the line.

d) Find the standard form of the equation of the line.

i) (2, 5) and (5, 7) ii) (-2, -1) and (2, -6)

iii) (5, 3) and (5, -3) iv) (-2, 5) and (3, 5)

Answer 1

Using points (2,5) and (5,7)

a) To find the slope of the line that passes through the given points, we must use our slope formula:

(y1 - y2) / (x1 - x2)

(7 - 5) / (5 - 2)

2/3 ≅ 0.667

b) Point-slope form of the equation of the line:

y - y1 = m * (x - x1)

y - (5) = (2/3)*(x - 2)

c) Slope-intercept form of the equation of the line:

y = mx + b

We will rearrange our equation in part b

y - 5 = (2/3)*(x-2)

y - 5 = (2/3)x - (4/3)

y = (2/3)x + 11/3

d) Standard form of the equation of the line:

Ax + By = C

We will rearrange our equation in part c

y = (2/3)x + 11/3

Multiply both sides by 3:

3y = 2x + 11

3y - 2x = 11