Graphing Linear Equations

Sec. 4.4 Slope- Intercept Form y = mx + b

1. y = 2x + 1
y-intercept: _____ slope: _____
2.
y-intercept: _____ slope: _____
3. x – y = 3
y-intercept: _____ slope: _____
4. 2x – 5y = 10
y-intercept: _____ slope: _____
5. 3x + 4y = 12
y-intercept: _____ slope: _____
6. 2x = y
y-intercept: _____ slope: _____

Finding the Slope

We can find the slope of a line if we know two of its points.
Use the slope formula ,, to find the slope of the line
containing these points:

1. (4, -3) and (2, 1)

2. (-5, -1) and (0, 2)

3. (1, 0) and (-1, 5)

4. (-2, -3) and (-2, 4)

5. (1, 3) and (4, 3)

Applications of Slope

Slope can also be thought of more informally as fol lows :

Use this idea to solve these problems:

1. The roof of a house rises 2.5 feet vertically for every
6 feet horizontally. Find the slope (or "pitch") of the
roof.

2. A road rises 50 ft for every 1500 ft of horizontal
distance. Find the slope (or "grade") of the road.

Sec. 4.5 Point-Slope Form

Given the right information, we can find not only the slope of a line, but also the entire equation.

Finding the Equation Given the Slope and Y-Intercept

The easiest scenario is if we are given the slope and y-intercept. We can then just plug these numbers into the slope -intercept form of an equation y = mx + b.

1. Find the equation of the line with slope = -3 and y-intercept = (0, 5)

2. Find the equation of the line with slope = 2/3 and y-intercept = (0, -4)

3. Find the equation of the line with slope = -0.78 and y-intercept = (0, 3.6)

Finding the Equation Given the Slope and One Point
If we are given the slope of a line and any one point on it, we
can find the equation using this formula:
Point-Slope Formula:

1. Find the equation of the line (in slope-intercept form) if
the slope is 3/4 and the line contains the point (2, 1).

2. Find the equation of the line (in slope-intercept form) if
the slope is -4 and the line contains the point (1, -3).

3. Find the equation of the line (in slope-intercept form) if
the slope is 1/3 and the line contains the point (-4, 2).

Finding the Equation Given Two Points
To find the equation of a line given two points, first find the
slope using Then use the point-slope formula,
to complete the process.

1. Find the equation of the line through the points
P₁(2, -3) and P₂(4, 1).

2. Find the equation of the line through the points
P₁(-1, 5) and P₂(7, 1).

3. Find the equation of the line through the points P₁(6, -4) and P₂(4, -2).

4. Find the equation of the line through the points P₁(3, -1) and P₂(0, -3).

Applications of Slope-Intercept

1. A sales associate is paid a base salary of $1400 per month plus a 3% commission on sales.

a. Let S = the amount of sales in one month, and G = the associate's gross salary. Write an equation in slope-intercept form describing the associate's gross salary as it depends on sales.

b. What will be the associate's gross salary if sales for the month are $15,600?

c. Graph the equation .