Vocabulary x-intercept y-intercept slope-intercept form

The x-intercept of a line is the x-coordinate of the point where the line intersects the x-axis. The y-coordinate of this point is always 0. The y-intercept of a line is the y-coordinate of the point where the line intersects the y-axis. The x-coordinate of this point is always 0.

Additional Example 1: Finding x- and y-intercepts Find the x- and y-intercepts. A. x y –2 –4 2 4 The line intersects the x-axis at (2,0). The x-intercept is 2. The line intersects the x-axis at (–4). The y-intercept is –4.

Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x- and y-intercepts. B. x y –2 –4 2 4 The line intersects the x-axis at (4,0). The x-intercept is 4. The line intersects the x-axis at (0, 1). The y-intercept is 1.

Find the x- and y-intercepts. A. Check It Out: Example 1 Find the x- and y-intercepts. A. x y –2 –4 2 4 The line intersects the x-axis at (1,0). The x-intercept is 1. The line intersects the x-axis at (–3). The y-intercept is –3.

Find the x- and y-intercepts. B. Check It Out: Example 1 Find the x- and y-intercepts. B. x y –2 –4 2 4 The line intersects the x-axis at (5,0). The x-intercept is 5. The line intersects the x-axis at (0, 2). The y-intercept is 2.

The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept of the line. y = mx + b Slope y-intercept

Additional Example 2A: Graphing by Using Slope and y-intercept Graph the equation. A. y = x + 1 1 3 Step 1: Find m and b. y = x + 1 1 3 m = 1 3 b = 1 Step 2: Plot (0, 1) Step 3: Use the slope to plot at least 1 more point on the line. 1 3

Additional Example 2A Continued Graph the equation. y = x + 1 1 3 x y –2 –4 2 4 Step 4: Draw a line through the points.

Since the y-intercept is 1, the point (0, 1) is a point on the line. Remember!

Additional Example 2: Graphing by Using Slope and y-intercept Graph the equation. B. 3x + y = 5 Step 1: Find m and b. 3x + y = 5 is not in the form y = mx+b, so solve for y. 3x + y = 5 – 3x = – 3x y = 5 – 3x y = –3x + 5 m = –3 b = 5

Additional Example 2B Continued Step 2: Plot (0, 5) Step 3: Use the slope –3 to plot at least 1 more point on the line. Step 4: Draw a line through the points.

Check It Out: Example 2A Graph the equation. y = x + 2 1 4 Step 1: Find m and b. y = x + 2 1 4 m = 1 4 b = 2 Step 2: Plot (0, 2) Step 3: Use the slope to plot at least 1 more point on the line. 1 4

Check It Out: Example 2A Continued Graph the equation. y = x + 2 1 4 x y –2 –4 2 4 Step 4: Draw a line through the points.

Check It Out: Example 2B Graph the equation. 2x + y = 4 Step 1: Find m and b. 2x + y = 4 is not in the form y = mx+b, so solve for y. 2x + y = 4 – 2x = – 2x y = 4 – 2x y = –2x + 4 m = –2 b = 4

Check It Out Example 2B Continued Step 2: Plot (0, 4) Step 3: Use the slope –2 to plot at least 1 more point on the line. Step 4: Draw a line through the points.

Additional Example 3: Writing an Equation in Slope-Intercept Form Write the equation of the line in slope-intercept form. The line falls from left to right so the slope is negative. m = rise run = - 2 5 The line intersects the y-axis at (0, -4), so the y-intercept is -4. b = –4 Substitute for m and b. y = 2 5 – x – 4

Check It Out: Example 3 Write the equation of the line in slope-intercept form. The line rises from left to right so the slope is positive. m = rise run = 1 2 The line intersects the y-axis at (0, 2), so the y-intercept is 2. b = 2 Substitute for m and b. y = 1 2 x + 2

Additional Example 4: Using Slope-Intercept Form A spider descends a 20-foot drainpipe at a rate of 2 feet per minute. The linear equation y = –2x + 20 represents the distance y the spider has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

Additional Example 4 Continued Spider's Decent Use the slope and y-intercept to graph the equation. 20 18 Plot (0, 20). Use the slope -2 to plot the line down to the x-axis. 16 14 12 Distance remaining (ft) The y-intercept is 20. This represents the total distance in feet the spider has to descend. 10 8 6 4 The x-intercept is 10. This represents the time in minutes it takes the spider has to descend the 20 ft. 2 2 4 6 8 10 12 14 16 Time (min)

Check It Out: Example 4 A submarine descends into a 40-mile sea cave at a rate of 5 miles per minute. The linear equation y = –5x + 40 represents the distance y the submarine has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

Check It Out: Example 4 Continued Use the slope and y-intercept to graph the equation. Submarine's Decent 45 Plot (0, 40). Use the slope -5 to plot the line down to the x-axis. 40 35 Distance remaining (mi) 30 The y-intercept is 40. This represents the total distance in feet the submarine has to descend. 25 20 15 10 The x-intercept is 8. This represents the time in minutes it takes the submarine to descend the 40 miles. 5 1 2 3 4 5 6 7 8 9 Time (min)

1. Graph y = x – 3. Identify the x- and y- intercepts. Lesson Quiz: Part I 3 8 1. Graph y = x – 3. Identify the x- and y- intercepts. x y –4 –8 4 8 x-int. = 8, y-int. = –3

2. Write the equation of the line in slope- intercept form. Lesson Quiz: Part II 2. Write the equation of the line in slope- intercept form. x y –4 –8 4 8 y = – x + 3 1 2

Lesson Quiz 3. A snail is crawling across a 15 mm long leaf. The snail crawls at a constant rate of 1 mm per second. The linear equation y = –x + 15 represents the distance y that the snail has left to crawl after x seconds. Graph the equation, and then identify the x- and y-intercepts and describe their meanings. y-int. = 15, total distance in mm that the snail has to crawl; x-int. = 15, time in seconds it takes the snail to crawl 15 mm.