12 3 Using Slopes and Intercepts 12 3

12. 3 Using Slopes and Intercepts

12. 3 Vocabulary 1 • In Linear Slope-Intercept Equation y = mx + b: – m is the slope – b is the y-intercept • The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0). Examples are (0, 6), (0, 99), or (0, -12).

12. 3 Vocabulary 2 • Besides y=mx+b, there is another form called Standard Form of a Linear Equation, which is Ax + By = C (and A, B and C are real numbers). • Standard Form is useful for finding intercepts. • A is the y-intercept and B is the x-intercept. • The x-intercept of a line is the value of x where the line crosses the x-axis (where y=0). Examples are (9, 0), (27, 0), or (-14, 0).

12. 3 Example 1 a • Find the x-intercept and y-intercept of the line 3 x + 4 y = 12. Use the intercepts to graph it. • Find the x-intercept (where y=0). • 3 x + 4 y = 12 • 3 x + 4(0) = 12 • 3 x/3 = 12/3 • x = 4, so x-intercept is 4 and is found at (4, 0).

12. 3 Example 1 b • • • Now find the y-intercept (where x = 0). 3 x + 4 y = 12 3(0) + 4 y = 12 4 y/4 = 12/4 y = 3, so y-intercept is 3 and is found at (0, 3).

12. 3 Example 1 c • Graph x-intercept (4, 0) and y-intercept (0, 3).

12. 3 Example 2 (y=mx+b) • Write the equation in slope-intercept form, then find the slope and y-intercept. • y = x – 6, rewrite equation to show each part • Y = (1)x + (-6) • So m = 1, and b = -6

12. 3 Example 3 (y=mx+b) • Write the equation in slope-intercept form, then find the slope and y-intercept. • 8 x = 5 y, rewrite so y is on the left side • 5 y = 8 x, now divide both sides by 5 • 5 y/5 = 8 x/5, now write in slope-intercept form • y = (8/5)x + (0) • m = 8/5, and b = 0

12. 3 Example 4 (y=mx+b) • Write the equation in slope-intercept form, then find the slope and y-intercept. • 3 x + 7 y = 9, subtract 3 x from both sides • 3 x – 3 x + 7 y = 9 – 3 x • 7 y = 9 – 3 x, rearrange Commutative property • 7 y = -3 x + 9, divide both sides by 7 • 7 y/7 = -3 x/7 + 9/7, write slope-intercept form • y = (-3/7)x + (9/7) • m = -3/7, and b = 9/7

12. 3 Example 5 a • The cash register deducts $2. 50 from a $20 gift card for each medium coffee purchased. Linear equation y = -2. 50 x + 20 shows y dollars on the card after x medium coffees purchased. Graph equation, explain slope and y-intercept. • If x=0, y=20, so (0, 20), & if x=8, y=0, so (8, 0) • m = -2. 50 dollars deducted per medium coffee purchased, and b = initial $20 on gift card.

12. 3 Example 5 b • Graph y = -2. 50 x + 20

12. 3 Example 6 • Write the equation of the line that passes thru (-3, 1) and (2, -1) in slope-intercept form.