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Graph Linear Equations Do Now Find the slope of each graph: 1. 2. Intercepts The place where a graph crosses over the x-axis is known as a x-intercept. Likewise, the place where a graph crosses over the y-axis is known as a y-intercept. Identify the x- and y-intercepts in the Do-Now graphs. Graph an Equation A linear equation can be written in slope-intercept form y = mx + b where m = slope and b is the y-intercept. Example: Find the slope and y-intercepts for the equations provided. Then graph the equation. y = 2x + 1 1 y = 3𝑥 – 3 y = -2x + 1 Graph Linear Equations Exercise: Graph a line with the information provided. Then state the equation of the line. 1. m = 1 and (-4, 2) Equation: 2 3 2. m = − and (-2, 1) Equation: 3. m = 3 and (2, 3) Equation: 2 Graph Linear Equations Notice that a linear equation in the slope-intercept form has a ‘y’ all by itself! Sometimes an equation needs to be rearranged so that we can reveal the true slope and y-intercept. Just like solving literal equations, keep your eye on the prize…get y by itself. Example: 2y + 3x = 8 Exercise: For each of the following, rearrange into y = mx + b form and then graph. 4. x + y = 4 5. x + 2y = 8 6. 3x – 4y = -4 7. 3y – 2x = -6 8. y = 4(x + 10) Graph Linear Equations Check points Sometimes a point won’t fit on the graph before you, but that doesn’t mean they don’t lie on the line (it does extend forever in both directions). Determine which points would 1 lie on the line 𝑦 = 2 𝑥 − 1 and which do not. (30, 14) (70, 28) (-30, -15) (-50, -26) Exercise: Circle all the ordered pairs (x, y) that are solutions to the provided equation. 9. 4x – y = 10 (3, 2) (2, 3) (-1, -14) (6, 0) (1, -6) Applications Gia had 25 songs in a playlist composed of songs from her two favorite artists, Beyonce and Jennifer Lopez. How many songs did she have by each on in the playlist? Equation: List three solutions: Exercise: Write an equation for each situation then graph it. 10. The sum of two numbers is 25. What are the numbers Graph Linear Equations Name: ___________________________________ Algebra I CC Date: ______ Exit Ticket 1 Consider the linear equation y = 3x – 1. 1. State the slope and y-intercept of this line. 2. Use the slope and the y-intercept to graph the line. Name: ___________________________________ Algebra I CC 1 Consider the linear equation y = 3x – 1. 1. State the slope and y-intercept of this line. 2. Use the slope and the y-intercept to graph the line. Date: ______ Exit Ticket Graph Linear Equations Name: ___________________________________ Algebra I CC Date: ______ HW #22 Lesson Summary An ordered pair is a solution to a two variable equation when each number substituted into its corresponding variable makes the equation a true number sentence. All of the solutions to a two variable equation are called a solution set. Directions: Graph the following linear equations. Be sure to state both the slope and yintercept. 1. y = − 3x + 3 4 2. 2y = x 3. 2x + y = 4 4. 3y + 12 = 2x Graph Linear Equations Review: 5. Solve for x: x4 – 1 = 15