Lesson 5-3 Slope-Intercept Form

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Objectives Write and graph linear equations in slope-intercept form Model real world data with an equation in slope-intercept form

Vocabulary Slope-intercept form - an equation of the form y = mx + b, where m is the slope and b is the y-intercept

x-y Coordinate Plane Point Plotting Quadrants II I III IV up 7 left 4 right 5 III IV down 8 (x, y) (-4, 7) (5, -8) x – left or right y – up or down

Example 1 Write an equation of the line whose slope is and whose y-intercept is –6. Slope-intercept form Replace m with and b with –6. Answer:

Example 2 Write an equation of the line shown in the graph. Step 1 You know the coordinates of two points on the line. Find the slope. Let

Example 2 cont Simplify. The slope is 2. Step 2 The line crosses the y-axis at (0, –3). So, the y-intercept is –3. Step 3 Finally, write the equation. Slope-intercept form Answer: The equation of the line is

Example 3 Graph Step 1 The y-intercept is –7. So graph (0, –7). y = 0.5x – 7 Step 2 The slope is 0.5 or From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3 Draw a line connecting the points.

Example 4 Graph Step 1 Solve for y to find the slope-intercept form. Original equation Subtract 5x from each side. Simplify. Divide each side by 4. Answer:

Example 4 cont Step 2 The y-intercept of is 2. So graph (0, 2). 5x + 4y = 8 Step 3 The slope is From (0, 2), move down 5 units and right 4 units. Draw a dot. Step 4 Draw a line connecting the points.

Example 5 Health The ideal maximum heart rate for a 25-year-old who is exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat. Words The rate drops 3 beats per minute every 5 years, so the rate of change is beats per minute each year. The ideal maximum heart rate for a 25-year-old is 117 beats per minute.

Example 5 cont Variables Let R = the ideal heart rate. Let a = years older than 25. Equation ideal rate Ideal rate of years older for 25- rate equals change times than 25 plus year-old. R a 117 Answer:

Example 5 cont Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old. The age 55 is 30 years older than 25. So, Ideal heart rate equation Replace a with 30. Simplify. Answer: The ideal heart rate for a 55-year-old person is 99 beats per minute.

Summary & Homework Summary: Homework: The linear equation y = mx + b is written in slope-intercept form, where m is the slope, and b is the y-intercept Slope-intercept form allows you to graph an equation quickly Homework: Pg. 275 14-32 even Pg. 831 1-12 all In almost all the chapter summaries of ch.5 there’s a graph!