1. 12.3 Using Slopes and Intercepts

2. 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).

3. 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).

4. 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).

5. 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).

6. 12.3 Example 1c
Graph x-intercept (4,0) and y-intercept (0,3).

7. 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

8. 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

9. 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

10. 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 = dollars deducted per medium coffee purchased, and b = initial $20 on gift card.

11. 12.3 Example 5b
Graph y = -2.50x + 20

12. 12.3 Example 6
Write the equation of the line that passes thru (-3,1) and (2,-1) in slope-intercept form.