Graph linear functions EXAMPLE 1 Graph the equation. Compare the graph with the graph of y = x. a.a. y = 2x b.b. y = x + 3 SOLUTION a.a. The graphs of.

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Presentation transcript:

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

Graph linear functions EXAMPLE 1 b.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.

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

Graph an equation in slope-intercept form EXAMPLE 2 STEP 3 Identify the slope. The slope is –, or, so plot 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). –

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

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

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

SOLUTION GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Compare the graph with the graph of y = x. 3. y = 4x 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.

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is +2, so plot the point (0, +2) where the line crosses the y- axis. STEP 2 Graph the equation 4. y = – x + 2

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Identify the slope. The slope is –1 so plot a second point on the line by starting at (0, 2) and then moving down 1 unit and right 1 unit. The second point is (1, 1). Draw a line through the two points. STEP 4

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is +4, so plot the point (0, +4) where the line crosses the y- axis. STEP 2 Graph the equation 5. y = x

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Draw a line through the two points. STEP 4 Identify the slope. The slope is so plot a second point on the line by starting at (0, 4) and then moving up 2 unit and right 5 unit. The second point is (5, 6). 2 5

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is –3, so plot the point (0, –3) where the line crosses the y- axis. STEP 2 Graph the equation 6. y = x – 3 1 2

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Draw a line through the two points. STEP 4 Identify the slope. The slope is so plot a second point on the line by starting at (0, –3) and then moving up 1 unit and right 2 unit. The second point is (–2, 2). 1 2

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is +5, so plot the point (0, +5) where the line crosses the y- axis. STEP 2 Graph the equation 7. y = 5 + x

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Identify the slope. The slope is 1 so plot a second point on the line by starting at (0, 5) and then moving up 1 unit and right 1 unit. The second point is (1, 6). Draw a line through the two points. STEP 4

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is +1, so plot the point (0, +1) where the line crosses the y- axis. STEP 2 Graph the equation 8. f (x) = 1 – 3x

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Identify the slope. The slope is –3 so plot a second point on the line by starting at (0, 1) and then moving down 3 unit and right 1 unit. The second point is (1, 2). Draw a line through the two points. STEP 4

GUIDED PRACTICE for Examples 1 and 2 SOLUTION The equation is already in slope-intercept form. STEP 1 Identify the y -intercept. The y- intercept is +10, so plot the point (0, +10) where the line crosses the y- axis. STEP 2 Graph the equation 9. f (x) = 10 – x

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Identify the slope. The slope is –1 so plot a second point on the line by starting at (0, 10) and then moving down 1 unit and right 1 unit. The second point is (1, 9). Draw a line through the two points. STEP 4