Unit 5: Analytic Geometry Unit 5: Review Consider this table of values. Does it represent a linear relationship? What is the slope? What is the y-intercept? What is the equation? Can you graph it?

Unit 5: Analytic Geometry Unit 5: Review Use the table of values to graph the line.

Unit 5: Analytic Geometry Unit 5: Review Learning Goals: I can find the slope between two points using a graph I know the formula for calculating the slope of a line I can use the formula to find the slope between two points.

Unit 5: Analytic Geometry Unit 5: Review The x-intercept is the point where the line crosses the x-axis. Its y-coordinate is 0.   The y-intercept is the point where the line crosses the y-axis. Its x-coordinate is 0. The y- intercept is represented by “b”

Unit 5: Analytic Geometry Unit 5: Review Remember all the different ways we can represent slope. m = slope Rise: The vertical distance between two points Run: The horizontal distance between two points m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 m = 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑦−𝑣𝑎𝑙𝑢𝑒𝑠 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑥−𝑣𝑎𝑙𝑢𝑒𝑠 m = ∆𝑦 ∆𝑥 m = 𝑦2−𝑦1 𝑥2−𝑥1

Unit 5: Analytic Geometry Unit 5: Review Remember that slope is a measure of the steepness of a line. As a line gets steeper its slope As a line becomes more flat its slope A line with a positive slope A line with a negative slope

Unit 5: Analytic Geometry Unit 5: Review Can you find the slope of this line?

Unit 5: Analytic Geometry Unit 5: Review Find the slope of the line that passes through the points (5, -2) and (3, 6)

Unit 5: Analytic Geometry Unit 5: Review Find the slope of the line that has an x-intercept of -5 and a y-intercept of 7.

Unit 5: Analytic Geometry Unit 5: Review Learning Goals: I can write the equation of a line given different pieces of information about the line.

Unit 5: Analytic Geometry Unit 5: Review The Equation of a Line is given by:   y = mx + b where “m” is the slope and “b” is the y-intercept.

Unit 5: Analytic Geometry Unit 5: Review Parallel lines have slopes that are the same. For example…. The line y = 3x – 6 is parallel to the line y = 3x + 1. I know because the slopes are the same. Perpendicular lines have slopes that are negative reciprocals. For example…. The line y = 7x + 2 is perpendicular to the line y = − 1 7 −3. 𝐼 know because the slopes are negative reciprocals.

Unit 5: Analytic Geometry Unit 5: Review Horizontal lines have a slope of zero. Their equations look like y = # Vertical lines have a slope that is undefined. Their equations look like x = #

Unit 5: Analytic Geometry Unit 5: Review Write the equation of a line that has a slope of 7 and a y-intercept of 9.

Unit 5: Analytic Geometry Unit 5: Review A line has an x-intercept of -3. and a slope of 4. What is the equation of the line?

Unit 5: Analytic Geometry Unit 5: Review Find the equation of the line that has a slope that is undefined and goes through the point (-4, -10).

Unit 5: Analytic Geometry Unit 5: Review Find the equation of the line that is passes through the point (2, -3) and is parallel to the line y = - 1 2 𝑥+9.

Unit 5: Analytic Geometry Unit 5: Review Find the equation of the line that passes through the point (-2, 6) and is perpendicular to y = 4x – 2.

Unit 5: Analytic Geometry Unit 5: Review What is the equation of a line that has a slope of zero and goes through the point (6, -5)?

Unit 5: Analytic Geometry Unit 5: Review Learning Goal I can interpret the meaning of slope and y-intercept for a variety of word problems.

Unit 5: Analytic Geometry Unit 5: Review Nico got a job wrapping presents over the holidays. The equation P = x + 50 represents his pay where P is his total pay per day and x is the number of presents he wraps. What is the slope and what does it represent? What is the y-intercept and what does it represent?

Unit 5: Analytic Geometry Unit 5: Review Nico got a job wrapping presents over the holidays. The equation P = x + 50 represents his pay where P is his total pay per day and x is the number of presents he wraps. c) How much would Nico get paid if he wrapped 300 presents?

Unit 5: Analytic Geometry Unit 5: Review Samantha purchased the original red ruby shoes worn by Dorothy in the Wizard of Oz. As the shoes are a collectible item they are expected to increase in value as represented by the equation V = 250,000 + 75t where V is the value of the shoes and t is the number of years since she purchased the shoes. What is the slope and what does it represent? What is the y-intercept and what does it represent?

Unit 5: Analytic Geometry Unit 5: Review Samantha purchased the original red ruby shoes worn by Dorothy in the Wizard of Oz. As the shoes are a collectible item they are expected to increase in value as represented by the equation V = 250,000 + 75t where V is the value of the shoes and t is the number of years since she purchased the shoes. c) How much will the shoes be worth in 15 years?

Unit 5: Analytic Geometry Unit 5: Review Learning Goal I can determine the rate of change of segments of a time-distance graph.

Unit 5: Analytic Geometry Unit 5: Review During which section of the graph does Rena travel the fastest? What do the negative slopes represent?

Unit 5: Analytic Geometry Unit 5: Review