When we are given two points, we can use the slope formula to find the slope of the line between them.

Example:You are given the points (4, 7) and (2, 6). Find

the slope.m = rise = y2 – y1 = 6 – 7 = 1

run x2 – x1 2 – 4 2

Step 1:Find the slope. Substitute the coordinates of the two

given points into the formula for slope, m = y2 – y1 x2 – x1

Step 2:Find the y-intercept. Substitute the slope m and the

coordinates of one of the points into the slope-intercept form, y = mx +b, and solve for the y-intercept.

Step 3:Write an equation of the line. Substitute the slope m

and the y-intercept b into the slope-intercept form, y = mx + b.

Write an of a line that passes through the points (3, 5) and (4, 7).First we must find the slope of the line. We need to

use the slope formula to do this.m = y2 – y1 = 7 – 5 = 2 = 2

x2 – x1 4 – 3 1

Now we must find the y-intercept.y = mx + b 5 = 2(3) + b5 = 6 + b Subtract 6 from both sides.-1 = b

Now let’s write the equation of the line.y = mx + by = 2x – 1

Write an equation of a line that passes through the points (9, 4) and (8, 7).First we must find the slope of the line. We need to

use the slope formula to do this.m = y2 – y1 = 7 – 4 = 3 = -3

x2 – x1 8 – 9 -1

Now we must find the y-intercept.y = mx + b 4 = -3(9) + b4 = -27 + b Add 27 to both sides.31 = b

Now let’s write the equation of the line.y = mx + by = -3x + 31

Write an equation of a line that passes through the points (6, 1) and (2, 4).First we must find the slope of the line. We need to

use the slope formula to do this.m = y2 – y1 = 4 – 1 = 3

x2 – x1 2 – 6 -4

Now we must find the y-intercept.y = mx + b 1 = (-3/4)(6) + b1 = -4.5 + b Add 4.5 to both sides.5.5 = b

Now let’s write the equation of the line.y = mx + by = (-3/4)x + 5.5

Two different nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other.

For example:The negative reciprocal of 4 is:

-1/4The negative reciprocal of -3 is:

1/3The negative reciprocal of -2/3 is:

3/2The negative reciprocal of 7/2 is:

-2/7

Using the figure to the left, show that two of the lines are perpendicular.

The slope of AB: m = 7 – 1 = 6 = 3

-4 + 8 4 2 The slope of BC:

m = 1 + 7 = 8 = 2 -8 -4 -12

-3 Notice that these two lines

have slopes that are negative reciprocals of each other. This means that they are perpendicular.

A (-4, 7)

B (-8, 1)

C (4, -7)

D (8, -1)

Write an equation of a line that is perpendicular to y = 6x – 3 and passes through the point (4, 5).

y = mx + b 5 = (-1/6)(4) + b5 = -2/3 + b17/3 = by = (-1/6)x + 17/3

Write an equation of a line that is perpendicular to y = (1/2)x + 3 and passes through the point (1, 4).

y = mx + b4 = -2(1) + b4 = -2 + b6 = by = -2x + 6