Vocabulary x-intercept y-intercept slope-intercept form Insert Lesson Title Here Course Using Slopes and Intercepts

You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0). Course Using Slopes and Intercepts

You MUST know this! Write this down! X-intercept, the y-value in the ordered pair is 0 ex: (4,0) which means the line crosses the x-axis at 4. Y-intercept, the x value in the ordered pair is 0! ex:(0,5) which means the line crosses the y-axis at 5.

To find the intercepts… To find the x-intercept, substitute 0 for y and solve the equation for x. The answer is your x-intercept. To find the y-intercept, substitute 0 for x and solve the equation for y. The answer is your y-intercept.

Find the x-intercept and y-intercept of the line 4x – 3y = 12. Use the intercepts to graph the equation. Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x-intercept (y = 0). 4x – 3y = 12 4x – 3(0) = 12 4x = 12 4x4x = x = 3 The x-intercept is 3. Course Using Slopes and Intercepts

Additional Example 1 Continued Find the y-intercept (x = 0). 4x – 3y = 12 4(0) – 3y = 12 –3y = 12 -3y = y = –4 The y-intercept is –4. Course Using Slopes and Intercepts

Additional Example 1 Continued The graph of 4x – 3y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4). Course Using Slopes and Intercepts

Find the x-intercept and y-intercept of the line 8x – 6y = 24. Use the intercepts to graph the equation. Try This: Example 1 Find the x-intercept (y = 0). 8x – 6y = 24 8x – 6(0) = 24 8x = 24 8x8x = x = 3 The x-intercept is 3. Course Using Slopes and Intercepts

Try This: Example 1 Continued Find the y-intercept (x = 0). 8x – 6y = 24 8(0) – 6y = 24 –6y = 24 -6y = y = –4 The y-intercept is –4. Course Using Slopes and Intercepts

Try This: Example 1 Continued The graph of 8x – 6y = 24 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4). Course Using Slopes and Intercepts

In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept. y = mx + b Slopey-intercept Course Using Slopes and Intercepts (X,Y) come from an ordered pair which lies on the line

For an equation such as y = x – 6, read the y- intercept as –6 and the slope as 1. Helpful Hint Course Using Slopes and Intercepts When asked to write the equation in slope- intercept form, simply solve for Y and put the ‘x’ term directly to the right of the = sign! This is logical if you look at the formula: y=mx+b What variable is isolated by itself on 1 side of the equation? YES, Y! Helpful Hint

Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y-intercepts Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 2x + y = 3 y = –2x + 3 The equation is in slope-intercept form. m = –2b = 3 Course Using Slopes and Intercepts

Additional Example 2B: Using Slope-Intercept Form to Find Slopes and y-intercepts B. 5y = 3x The equation is in slope-intercept form. b = 0 y = x m = 3 5 Course Using Slopes and Intercepts

Additional Example 2C: Using Slope-Intercept Form to Find Slopes and y-intercepts C. 4x + 3y = 9 b = 3 y =- x m =- 4 3 The equation is in slope-intercept form. Course Using Slopes and Intercepts

Try This: Example 2A Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 4x + y = 4 y = –4x + 4The equation is in slope-intercept form. m = –4b = 4 Course Using Slopes and Intercepts

Try This: Example 2B B. 7y = 2x 7y = 2x The equation is in slope-intercept form. b = 0 y = x m = 2 7 Course Using Slopes and Intercepts

Try This: Example 2C C. 5x + 4y = 8 5x + 4y = 8 b = 2 y =- x The equation is in slope-intercept form. m =- 5 4 Course Using Slopes and Intercepts

Additional Example 3: Entertainment Application A video club charges $8 to join, and $1.25 for each DVD that is rented. The linear equation y = 1.25x + 8 represents the amount of money y spent after renting x DVDs. Graph the equation by first identifying the slope and y-intercept. y = 1.25x + 8 The equation is in slope-intercept form. b = 8m =1.25 Course Using Slopes and Intercepts NOTE that the initial value is the same as the y-intercept. Initial value in this case is the upfront charge. (Initial, what you start with)

Additional Example 3 Continued The slope of the line is 1.25, and the y-intercept is 8. The line crosses the y-axis at the point (0, 8) and moves up 1.25 units for every 1 unit it moves to the right. Course Using Slopes and Intercepts

Try This: Example 3 A salesperson receives a weekly salary of $500 plus a commission of 5% for each sale. Total weekly pay is given by the equation S = 0.05c Graph the equation using the slope and y-intercept. y = 0.05x The equation is in slope-intercept form. b = 500 (initial value)m =0.05 Course Using Slopes and Intercepts

Try This: Example 3 Continued The slope of the line is 0.05, and the y-intercept is 500. The line crosses the y-axis at the point (0, 500) and moves up 0.05 units for every 1 unit it moves to the right. x y , ,000 Course Using Slopes and Intercepts 250/5000=.05

Question time! Can you find the x-intercept and y-intercepts of a line? Can you graph the intercepts and draw the graphed line? Can you solve an equation and write it in slope-intercept form? Do you know the equation for slope-intercept form? What do ‘m’, ‘b’, ‘x’ & ‘y’ stand for in the slope intercept form equation? Parallel lines have what kind of slope? Perpendicular lines have what kind of slope? What is the slope formula given 2 ordered pair? If you can answer these questions then you’re ready! If not, raise both arms NOW!

What is the equation of the line? The formula for slope-intercept form has 3 names. The formula y=mx+b is called: 1 st name: Slope-Intercept Form 2 nd name: Equation of a line 3 rd name: Standard Form Anytime you are asked to write an equation in slope-intercept form, the equation of a line or standard form, write the equation in y=mx+b form!

So, let’s put what we know so far together… Given 2 ordered pair and asked to find the equation of the line: (y=mx+b) Step 1: use the slope formula and find the slope. Step 2: use the slope intercept formula and plug in the slope and 1 ordered pair and solve the equation for b which is the y-intercept. Step 3: plug in the slope and y-intercept, leave x and y in the equation and write your answer. (example: y=3x+4)

Additional Example 4: Writing Slope-Intercept Form Write the equation of the line that passes through (3, –4) and (–1, 4) in slope-intercept form. Find the slope. The slope is –2. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b 4 = –2(–1) + b 4 = 2 + b Substitute –1 for x, 4 for y, and –2 for m. Simplify. 4 – (–4) –1 – 3 = y 2 – y 1 x 2 – x 1 8 –4 = = –2 Course Using Slopes and Intercepts

Additional Example 4 Continued Solve for b. Subtract 2 from both sides. Write the equation of the line, using –2 for m and 2 for b. 4 = 2 + b –2 2 = b y = –2x + 2 Course Using Slopes and Intercepts Great job! You did it! What is the slope? What is the y- intercept? What does the graphed line look like?

Try This: Example 4 Write the equation of the line that passes through (1, 2) and (2, 6) in slope-intercept form. Find the slope. The slope is 4. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b 2 = 4(1) + b 2 = 4 + b Substitute 1 for x, 2 for y, and 4 for m. Simplify. 6 – 2 2 – 1 = y 2 – y 1 x 2 – x = = 4 Course Using Slopes and Intercepts

Try This: Example 4 Continued Solve for b. Subtract 4 from both sides. Write the equation of the line, using 4 for m and –2 for b. 2 = 4 + b –4 –2 = b y = 4x – 2 Course Using Slopes and Intercepts You did it again! What is the slope? What is the y-intercept? What does the graphed line look like?

Lesson Quiz Write each equation in slope-intercept form, and then find the slope and y-intercept. 1. 2y – 6x = –10 2. –5y – 15x = 30 Write the equation of the line that passes through each pair of points in slope- intercept form. 3. (0, 2) and (4, –1) 4. (–2, 2) and (4, –4) y = –3x – 6; m = –3; b = –6 y = 3x – 5; m = 3; b = –5 Insert Lesson Title Here y = –x y = – x Course Using Slopes and Intercepts