1. Warm Up #8 Evaluate each expression for x = –1, 0, and 2. 1. 2x + 3 2.
– 1
ANSWER – 5 3
, –1, 1
ANSWER
1, 3, 7

4. Graphing Lines Method 1: From the slope-intercept form y = mx + b
Ex. Graph y = 2x - 3 1
y axis
Start on the y axis
Go from that point up or down (depending if it’s – or +) the numerator, then over to the right the denominator
x axis
In this case, up two, over one
Draw a line through the two points

5. Graph both lines on the same graph: y = -2x + 4 and y = 3x - 2

6. Graph both lines on the same graph: y = -¾x – 2 and y = -¾x + 2
Same slope: Parallel Lines

7. Graph both lines on the same graph: y = ½x – 2 and y = -2x + 2
Negative Reciprocal slopes: Perpendicular Lines Lines

8. GUIDED PRACTICE
for Examples 1 and 2
Graph the equation. Compare the graph with the graph of y = x. 2.
y = x – 2
SOLUTION
y = x
The graphs of y = x – 2 and
y = x both have a slope of 1,
but the graph of y = x – 2 has a
y-intercept of –2 instead of 0.
y = x - 2

9. GUIDED PRACTICE
for Examples 1 and 2
Graph the equation. Compare the graph with the graph of y = x. 3.
y = 4x
SOLUTION
y = x
The graphs of y = 4x and y = x
both have a y-intercept of 0,
but the graph of y = 4x has a
slope of 4 instead of 1.
y = 4x

10. GUIDED PRACTICE for Examples 1 and 2 Graph the equation 2 5. y = x + 4

11. GUIDED PRACTICE for Examples 1 and 2 Graph the equation
9. f (x) = -2 + x
8. f (x) = 1 – 3x
f(x) = x – 2
f(x) = -3x + 1

12. EXAMPLE 3
Solve a multi-step problem
Biology
The body length y (in inches) of a walrus calf can be modeled by y = 6x + 48 where x is the calf’s age (in months).
• Graph the equation.
• Describe what the slope and y-intercept represent in this situation.
• Use the graph to estimate the body length of a calf that is 10 months old.

13. y = 6x + 48 EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1
Graph the equation.
(2 , 60)
y = 6x + 48
(0 , 48)
STEP 2
Interpret the slope and y-intercept. The slope, 6, represents the calf’s rate of growth in inches per month. The y - intercept, 48, represents a newborn calf’s body length in inches.

14. EXAMPLE 3
Solve a multi-step problem
STEP 3
Estimate the body length of the calf at age 10 months by starting at 10 on the x-axis and moving up until you reach the graph. Then move left to the y-axis.At age 10 months, the body length of the calf is about 115 inches.

15. Method 2: Using two intercepts from Standard Form ax + by = c
Graph: 3x + 4y = -12
x intercept ( , 0 ) let y = 0 and solve for x -4
3x + 4(0) = -12
3x = -12
x = -12
= - 4 3
y intercept ( 0 , ) let x = 0 and solve for y -3
3(0) + 4y = -12
4y = -12
y = -12
= - 3 4

16. After finding the two intercepts, plot both points on the graph and draw a line through them
x intercept ( -4 , 0 )
y intercept ( 0 , -3 )

17. Graph both lines on the same graph: 3x – 2y = 6 and 5x + 2y = 10
x int. ( , 0 ) 2
y int. ( 0 , ) -3
Line 2:
x int. ( , 0 ) 2
y int. ( 0 , ) 5

18. EXAMPLE 5
Graph horizontal and vertical lines
Graph (a) y = 2 and (b) x = –3.
SOLUTION
a. The graph of y = 2 is the horizontal line that passes through the point (0, 2). Notice that every point on the line has a y-coordinate of 2.
b. The graph of x = –3 is the vertical line that passes through the point (–3, 0). Notice that every point on the line has an x-coordinate of –3.

19. GUIDED PRACTICE for Examples 4 and 5 Graph the equation. 14. y = –4

21. Write an equation given the slope and y-intercept
EXAMPLE 1
Write an equation given the slope and y-intercept
SOLUTION
Given the y-intercept is -2 and the slope is ¾ Use the
slope-intercept form to write an equation of the line
y = mx + b
Use slope-intercept form.
y = x + (–2) 3 4
Substitute for m and –2 for b. 3 4 3 4
y = x – 2
Simplify.

22. GUIDED PRACTICE
for Example 1
Write an equation of the line that has the given slope and y-intercept.
1. m = 3, b = 1
3. m = – , b = 3 4 7 2
ANSWER
ANSWER
y = – x + 3 4 7 2
y = x + 1 3
2. m = –2 , b = –4
ANSWER
y = –2x – 4

23. To write the equation of a line in slope-intercept form y = mx + b
x y1
Point ( , )
Slope m =
Identify a point and a slope
Substitute values into point-slope form
Solve for y
y – y1 = m(x – x1)
y = mx + b
Answer will be in slope-intercept form
Write an equation given the slope and a point

24. Write the equation of the line with the given information shown
x y1
Point ( , )
Slope m =
Write the equation of the line with the given information shown
3/4
y – y1 = m(x – x1)
Identify a point and a slope
Substitute values into point-slope form
Solve for y
y – (-2) = 3/4(x – 4)
y + 2 = 3/4x – 3
y = 3/4x – 5

25. Write an equation given the slope and a point
EXAMPLE 2
Write an equation given the slope and a point
Write an equation of the line that passes through (5, 4) and has a slope of –3.
x y1
Point ( , )
Slope m = -3
y – y1 = m(x – x1)
y – 4 = –3(x – 5)
y – 4 = –3x + 15
y = –3x + 19

26. Write equations of parallel or perpendicular lines EXAMPLE 3
Write an equation of the line that passes through (–2,3) and is (a) parallel to the line y = –4x + 1.
x y1
Point ( , )
Slope m =
Remember: Parallel lines have the same slope -4
y – y1 = m(x – x1)
y – 3 = –4(x – (-2))
y – 3 = –4(x + 2))
y – 3 = –4x – 8
y = –4x – 5

27. ¼ Write equations of parallel or perpendicular lines EXAMPLE 3
Write an equation of the line that passes through (–2,3) and is (b) perpendicular to, the line y = –4x + 1.
x y1
Point ( , )
Slope m =
Remember: Perpendicular lines have the negative reciprocal slopes
y – y1 = m(x – x1)
y – 3 = ¼(x – (-2))
y – 3 = ¼(x + 2))
y – 3 = ¼x + ½
y = ¼x + 3 ½

28. EXAMPLE 4
Write an equation given two points
Write an equation of the line that passes through (5, –2)
and (2, 10).
SOLUTION
The line passes through (x1, y1) = (5,–2) and
(x2, y2) = (2, 10). Find its slope.
y2 – y1
m =
x2 – x1
10 – (–2) =
2 – 5 12 –3
= –4

29. Write an equation given two points
EXAMPLE 4
Write an equation given two points
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line.
x y1
Point ( , )
Slope m = -4
y – y1 = m(x – x1)
y – 10 = – 4(x – 2)
y – 10 = – 4x + 8
y = – 4x + 18

30. Classwork
Workbook 2-3 (1-30 multiples of 3) Workbook 2-4 (1-23 odd)