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

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

12.3 Example 1c 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. 8x = 5y, rewrite so y is on the left side 5y = 8x, now divide both sides by 5 5y/5 = 8x/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. 3x + 7y = 9, subtract 3x from both sides 3x – 3x + 7y = 9 – 3x 7y = 9 – 3x, rearrange Commutative property 7y = -3x + 9, divide both sides by 7 7y/7 = -3x/7 + 9/7, write slope-intercept form y = (-3/7)x + (9/7) m = -3/7, and b = 9/7

12.3 Example 5a The cash register deducts $2.50 from a $20 gift card for each medium coffee purchased. Linear equation y = -2.50x + 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 5b Graph y = -2.50x + 20

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