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## Warm Up

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**Warm Up**Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 Solve each equation for y. 3. y –6x = 9 b = –6 2.m = –1, x = 5, and y = –4 b = 1 y = 6x + 9 4. 4x –2y = 8 y = 2x – 4**3-6**§ 3.6, Lines in the Coordinate Plane Holt McDougal Geometry Holt Geometry**Learning Targets**I will graph lines and write their equations in slope-intercept and point-slope form. I will classify lines as parallel, intersecting, or coinciding.**Vocabulary**point-slope form slope-intercept form**point-slope form:**slope-intercept form:**Remember!**A line with y-intercept b contains the point (0, b). A line with x-intercept a contains the point (a, 0).**Example 1A: Writing Equations In Lines**Write the equation of the line in slope-intercept form that passes through the points (-1, 0) and (1, 2). Solution: y = mx + b 0 = 1(-1) + b 1 = b y = x + 1**5**y – 0 = (x – 3) 3 5 y = (x - 3) 3 Example 1B: Writing Equations In Lines Write the equation of the line in point-slope form that has the x-intercept 3 and y-intercept -5. y –y1 = m(x – x1)**The equation is given in the slope-intercept form, with a**slope of and a y-intercept of 1. Plot the point (0, 1) and then rise 1 and run 2 to find another point. Draw the line containing the points. run 2 rise 1 (0, 1) Example 2A: Graphing Lines Graph each line.**The equation is given in the point-slope form, with a slope**of through the point (–4, 3). Plot the point (–4, 3) and then rise –2 and run 1 to find another point. Draw the line containing the points. rise –2 (–4, 3) run 1 Example 2B: Graphing Lines Graph each line. y – 3 = –2(x + 4)**(0, –3)**Example 2C: Graphing Lines Graph each line. y = –3 The equation is given in the form of a horizontal line with a y-intercept of –3. The equation tells you that the y-coordinate of every point on the line is –3. Draw the horizontal line through (0, –3).**(0, –4)**Example 2D:Graphing Lines Graph each line. y = –4 The equation is given in the form of a horizontal line with a y-intercept of –4. The equation tells you that the y-coordinate of every point on the line is –4. Draw the horizontal line through (0, –4).**A system of two linear equations in two variables represents**two lines. Three conditions exist when graphing two lines: parallel intersecting coinciding (same line, but equations may be written in different forms)**The equations of lines that coincide can be simplified to be**exactly the same in the same format. Many times, they are written in different forms.**Example 3A: Classifying Pairs of Lines**Determine whether the lines are parallel, intersect, or coincide. y = 3x + 7, y = –3x – 4 The lines have different slopes, so they intersect.**Both lines have a slope of , and the y-intercepts are**different. So the lines are parallel. Example 3B: Classifying Pairs of Lines Determine whether the lines are parallel, intersect, or coincide. Solve the second equation for y to find the slope-intercept form. 6y = –2x + 12**Example 3C: Classifying Pairs of Lines**Determine whether the lines are parallel, intersect, or coincide. 2y – 4x = 16, y – 10 = 2(x - 1) Solve both equations for y to find the slope-intercept form. 2y – 4x = 16 y – 10 = 2(x – 1) 2y = 4x + 16 y – 10 = 2x - 2 y = 2x + 8 y = 2x + 8 Both lines have a slope of 2 and a y-intercept of 8, so they coincide.**Critical Thinking:**Erica is trying to decide between two car rental plans. For how many miles will the plans cost the same?**1**Understand the Problem The answer is the number of miles for which the costs of the two plans would be the same. Plan A costs $100.00 for the initial fee and $0.35 per mile. Plan B costs $85.00 for the initial fee and $0.50 per mile.**Make a Plan**2 Write an equation for each plan, and then graph the equations. The solution is the intersection of the two lines. Find the intersection by solving the system of equations.**3**Solve 0 = –0.15x + 15 Plan A: y = 0.35x + 100 Plan B: y = 0.50x + 85 Subtract the second equation from the first. x = 100 Solve for x. Substitute 100 for x in the first equation. y = 0.50(100) + 85 = 135**3**Solve Continued The lines cross at (100, 135). Both plans cost $135 for 100 miles.**Look Back**4 Check your answer for each plan in the original problem. For 100 miles, Plan A costs $100.00 + $0.35(100) = $100 + $35 = $135.00. Plan B costs $85.00 + $0.50(100) = $85 + $50 = $135, so the plans cost the same.**Check It Out! Example 4**What if…? Suppose the rate for Plan B was also $35 per month. What would be true about the lines that represent the cost of each plan? The lines would be parallel.