EXAMPLE 1 Graph linear functions Graph the equation

EXAMPLE 1 Graph linear functions b. The graphs of y = x + 3

EXAMPLE 2 Graph y = – Graph an equation in slope-intercept form 2 x

EXAMPLE 2 Graph an equation in slope-intercept form STEP 3 2 , or ,

EXAMPLE 2 Graph an equation in slope-intercept form STEP 4 Draw a line through

GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Compare the graph with

GUIDED PRACTICE for Examples 1 and 2 Graph the equation 4. y = –x

GUIDED PRACTICE for Examples 1 and 2 Graph the equation 6. y= 1 x–

GUIDED PRACTICE for Examples 1 and 2 Graph the equation 8. f (x) =

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EXAMPLE 1 Graph linear functions Graph the equation. Compare the graph with the graph of y = x. b. y = x + 3 a. y = 2 x SOLUTION a. The graphs of y = 2 x and y = x both have a y-intercept of 0, but the graph of y = 2 x has a slope of 2 instead of 1.

EXAMPLE 1 Graph linear functions b. The graphs of y = x + 3 and y = x both have a slope of 1, but the graph of y = x + 3 has a y-intercept of 3 instead of 0.

EXAMPLE 2 Graph y = – Graph an equation in slope-intercept form 2 x – 1. 3 SOLUTION STEP 1 The equation is already in slope-intercept form. STEP 2 Identify the y-intercept. The y-intercept is – 1, so plot the point (0, – 1) where the line crosses the y-axis.

EXAMPLE 2 Graph an equation in slope-intercept form STEP 3 2 , or , – 2 so plot 3 3 a second point on the line by starting at (0, – 1) and then moving down 2 units and right 3 units. The second point is (3, – 3). Identify the slope. The slope is –

EXAMPLE 2 Graph an equation in slope-intercept form STEP 4 Draw a line through the two points.

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

GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Compare the graph with the graph of y = x. 2. y = x – 2 SOLUTION 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.

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

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

GUIDED PRACTICE for Examples 1 and 2 Graph the equation 6. y= 1 x– 3 2 7. y=5+x

GUIDED PRACTICE for Examples 1 and 2 Graph the equation 8. f (x) = 1 – 3 x 9. f (x) = 10 – x