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

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