Algebra 1B Chapter 4 Notes

4.1—The Coordinate Plane In your groups, huddle up and discuss the following topic on the next slide.

The Coordinate Plane When we take two lines and intersect them in the middle, we have created a coordinate plane A coordinate plane has an x-axis (horizontal) and a y-axis (vertical).

Points move along the x-axis from left to right. Points move along the y-axis up and down. Where the two axes meet is called the origin. The origin is considered the point (0,0)

In terms of the x-axis, if a point moves to the left then the x-value is negative. In terms of the x-axis, if a point moves to the right then the x-value is positive.

In terms of the y-axis, if a point moves down then the y-value is negative. In terms of the y-axis, if a point moves up then the y-value is positive.

A point is classified as (x,y) In other words, we move to the left or the right first then we move up or down. What does it mean if a point is (4,-2)?

The coordinate plane is split into four quadrants. By knowing our four quadrants, when asked to plot a point, we can tell which quadrant it is in.

In quadrant 1, both x and y are positive In quadrant 2, x is negative and y is positive In quadrant 3, both x and y are negative In quadrant 4, x is positive and y is negative. All points sit in one of four quadrants (unless x or y equals 0)

Example In which quadrant do the following points sit: A (2, 3) B (-3, 4) C (-8, 0) D (-1, -1)

Team Huddle In which quadrant do the following points sit: A (4, -13) B (5, 5) C (-2, 6) D (0, 4)

4.2—Graphing Linear Equations In your groups, huddle up, and answer the following questions: plot the following points on a coordinate plane: (0, -1), (1, 1), (2, 3), (-1, -3) 3x + 3y = 9. Get y by itself.

When we plot points, we have an x-value and a y-value. If we connect enough points together, we could create a line. Lines are known as linear equations. An ordered pair that makes a linear equation true is a solution of an equation.

Example Prove that (1,2) is a solution of x + 2y = 5.

Team Huddle Prove that (4, -1) is a solution of x + 5y = 3

Example Find three ordered pairs that are solutions of -2x + y = -3

Team Huddle Find three ordered pairs that are solutions of 2x + y = 8

Example Use a table of values to graph y = 2x + 1 (HINT: When the number in front of x is a whole number, use 0, 1, and -1)

Example Use a table of values to graph (HINT: When the number in front of x is a fraction, use the denominator, its inverse, and 0)

Team Huddle Use a table of values to graph y = 4x - 3

Example Use a table of values to graph 4x + 2y = 8 HINT: Same setup as before, except we have to get y by itself.

Recap In order to graph a linear equation, there are three steps we have to follow: 1. Rewrite the equation in slope-intercept form (get y by itself) 2. Choose three values for x, substitute them into the equation, and solve. 3. Plot points and connect.

4.7—Graphing Lines Using Slope-Intercept Form In your groups, huddle up, and graph the following linear equation:

While we can graph a linear equation by using tables, there are other ways to graph lines. One such way is through identifying the slope and the intercept. Slope-intercept form: y = mx + b

In slope-intercept form, the variable m represents the slope and the variable b represents the y-intercept. The y-intercept is where a linear equation crosses the y-axis. NOTE: If there is no y-intercept, it crosses the y-axis at 0. The slope represents the rate of change.

In looking at slope, it generally is in fraction form So if the slope were 2/3, we would move up 2 and to the right 3.

If the slope is a whole number, then that number becomes the a term and 1 becomes the b term. After moving up or down, we would move one to the right.

Example Graph the following equation using slope-intercept form.

Team Huddle Graph the following equation using slope-intercept form

Example Graph the following equation using slope-intercept form 2x + 4y = 8

Team Huddle Graph the following equation using slope-intercept form 4x – 3y = 12