You found the slopes of lines.

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Parallel and Perpendicular Lines

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You found the slopes of lines. Write an equation of a line given information about the graph. Solve problems by writing equations. Then/Now

slope-intercept form point-slope form Vocabulary

Concept

y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3 Slope and y-intercept Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3 y = 6x – 3 Simplify. Example 1

Plot a point at the y-intercept, –3. Slope and y-intercept Answer: Plot a point at the y-intercept, –3. Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept. Draw a line through these two points. Example 1

Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4. A. x + y = 4 B. y = x – 4 C. y = –x – 4 D. y = –x + 4 Example 1

Slope and a Point on the Line Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line. Point-slope form Simplify. Example 2

Graph the given point (–10, 8). Slope and a Point on the Line Answer: Graph the given point (–10, 8). Use the slope to find another point 3 units down and 5 units to the right. Draw a line through these two points. Example 2

Write an equation in point-slope form of the line whose slope is that contains (6, –3). B. C. D. Example 2

Step 1 First, find the slope of the line. Two Points A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Step 1 First, find the slope of the line. Slope formula x1 = 4, x2 = –2, y1 = 9, y2 = 0 Simplify. Example 3

Distributive Property Two Points Step 2 Now use the point-slope form and either point to write an equation. Point-slope form Using (4, 9): Distributive Property Add 9 to each side. Answer: Example 3

Step 1 First, find the slope of the line. Two Points B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Step 1 First, find the slope of the line. Slope formula x1 = –3, x2 = –1, y1 = –7, y2 = 3 Simplify. Example 3

Distributive Property Two Points Step 2 Now use the point-slope form and either point to write an equation. Point-slope form Using (–1, 3): m = 5, (x1, y1) = (–1, 3) Distributive Property Add 3 to each side. y = 5x + 8 Answer: Example 3

A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). B. C. D. Example 3a

B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10). A. y = 2x – 3 B. y = 2x + 1 C. y = 3x – 2 D. y = 3x + 1 Example 3b

This is a horizontal line. Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Step 1 Slope formula This is a horizontal line. Example 4

Subtract 2 from each side. y = –2 Horizontal Line Step 2 Point-Slope form m = 0, (x1, y1) = (5, –2) Simplify. Subtract 2 from each side. y = –2 Answer: Example 4

Write an equation of the line through (–3, 6) and (9, –2) in slope-intercept form. B. C. D. Example 4

Concept

y = mx + b Slope-Intercept form 0 = –5(2) + b m = –5, (x, y) = (2, 0) Write Equations of Parallel or Perpendicular Lines y = mx + b Slope-Intercept form 0 = –5(2) + b m = –5, (x, y) = (2, 0) 0 = –10 + b Simplify. 10 = b Add 10 to each side. Answer: So, the equation is y = –5x + 10. Example 5

A. y = 3x B. y = 3x + 8 C. y = –3x + 8 D. Example 5