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Chapter 5/ Algebra Name:
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Goal: Use the slope intercept form to write an equation of a line. Slope-‐Intercept Form The slope-‐intercept form of the equation of a line with slope m and y intercept b is y = mx + b Example 1: Equation of a Line Write an equation of the line whose slope is 4 and whose y-intercept is -3. Steps: 1. Write the slope intercept form. y= mx + b 2. Substitute slope _____ for m and ____ for b. y + _____x + ______ 3. Simplify the equation. y = Answer: The equation of the line is y = ____________________ Example 2: Equation of a Line Write an equation of the line whose slope is 4 and the y-intercept is 7. Steps: 1. Write the slope intercept form. y= mx + b 2. Substitute slope _____ for m and ____ for b. y + _____x + ______ 3. Simplify the equation. y = Answer: The equation of the line is y = ____________________ Checkpoint: Write an equation of the line in slope-‐intercept form. 1. The slope is 2 and the 2. The slope is -‐5 and the y-‐intercept is 10. y-‐intercept is 1.
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Example 3: Write the equation of the line whose slope is ½ and the y-intercept is 0.5
Steps: 1. Write the slope intercept form. y= mx + b 2. Substitute slope _____ for m and ____ for b. y + _____x + ______ 3. Simplify the equation. y = Answer: The equation of the line is y = ____________________ Example 4: Write the equation of the line whose slope is -3/5 and the y-intercept is -2.75 Steps: 1. Write the slope intercept form. y= mx + b 2. Substitute slope _____ for m and ____ for b. y + _____x + ______ 3. Simplify the equation. y = Answer: The equation of the line is y = ____________________ Checkpoint: Write an equation of the line in slope-intercept form. 1. The slope is 2/3 2. The slope is -‐5/7 and the and the y-‐intercept is 5.5. y intercept is -‐0.2
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Goal: Use point-‐slope form to write the equation of a line. Point Slope Form:
Example 1: Write the equation of the line in the graph in point slope form. 1. Use the given point from the graph: (___,___) 2. From the graph find slope. m = 3. y – y1 = m(x – x1) 4. y -‐ ____ = ___ ( x -‐ ___) Example 2: Write the equation of the line in the graph in point-slope form. Point: Slope: Plug in to formula.
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Checkpoint: Write each of these graphs in point-slope form. Point: Point: Slope: Slope: Equation: Equation: Example 3: Write in point-slope form the equation of the line that passes through the point (2, -4) with the slope of 5. Solution 1. Write the point slope form.
2. Substitute ___ for x1 and ___ for y1, and ____ for m. 3. Simplify the equation.
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Example 4: (-3, -1) m= ½
1. Write the point slope form.
2. Substitute ___ for x1 and ___ for y1, and ____ for m. 3. Simplify the equation
Checkpoint: Write in point-slope form. a. (-‐3, -‐5), m = 2 b. (-‐1, 9), m = -‐2
Goal: To put an equation into point slope form and solve. Example 1: Write in slope intercept form the equation of the line that passes through the point (-2, 5) with a slope -3. Solution. 1. Write the point-‐slope form.
2. Substitute ____ for x1, ___ for y1, and ___ for m.
3. Simplify the equation.
4. Distribute the ____.
5. Add ___ to each side.
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Example 2: Write in slope intercept form. (3, 4) m = ¾ 1. Write the point-‐slope form.
2. Substitute ____ for x1, ___ for y1, and ___ for m.
3. Simplify the equation.
4. Distribute the ____.
5. Add ___ to each side.
Example 3: Write in slope intercept form. (0, 1) m = ½ 1. Write the point-‐slope form.
2. Substitute ____ for x1, ___ for y1, and ___ for m.
3. Simplify the equation.
4. Distribute the ____.
Add ___ to each side. Checkpoint: Write in slope intercept form. a. (-‐3, -‐5) m = 2 b. (-‐1, 9) m = -‐2
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How do you know when to graph using standard form and when to use point-slope form? 1. Standard Form 2. Point-‐Slope Form y = mx + b y – y1 = m (x – x1) if you are given the slope m if you are given the and the y-‐intercept slope m and a point (x1, y1) Which form would you use to graph the following information? Decide then put into proper format to graph. 1. m = ½, y-‐int = 4 2. m = -‐3/4, (4, 5)
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Review: Graphing using standard form or point slope form. Standard Form Point-‐ Slope Form m = -‐1/2 (2, 0) m = -‐1/2 (1, 2)
Goal: Write an equation of a line given two points on the line. Example 1: Use a graph. The line at the right models a snowboarder’s descent down a mountain. Write the equation of the line in slope-intercept form. Solution 1. Find the slope.
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2. Write the equation of the line. From the graph you can see the y-‐intercept is b = ____. Use the slope-‐intercept form. plug in _____ for m and ____ for b.
Example 2: Solution 1. Find the slope.
2. Write the equation of the line. From the graph you can see the y-‐intercept is b = ____. Use the slope-‐intercept form. plug in _____ for m and ____ for b. Checkpoint: Write the equation of the line in slope-‐intercept form.
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1. Find the slope 2. Write the equation of the line
a. Use slope-intercept form if you know the y-intercept
b. Use point-slope form if you do not know the y-intercept.
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Example 3: Write an Equation of a Line Given Two Points Write in slope-intercept form the equation of the line that passes through the points (2, 8) and (-5, 1) Solution 1. Find the slope. 2. Use (x1, y1) = (2, 8) and (x2, y2) = (-‐5, 1)
3. Write the formula for slope. 4. Substitute and solve
5. Write the equation of the line. Use point-‐slop form, because you do not know the y-‐intercept.
6. Write point-‐slope form.
7. Substitute ___ for m, ___ for x1, and ____ for y1
8. Use distributive property 9. Add ___ to each side.
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Example 4: Put into slope intercept format. Points: (-7, 3), (-4, 1) Solution 1. Find the slope. 2. Use (x1, y1) = (___, _____) and (x2, y2) = (____, ____)
3. Write the formula for slope. 4. Substitute and solve
5. Write the equation of the line. Use point-‐slop form, because you do not know the y-‐intercept.
6. Write point-‐slope form.
7. Substitute ___ for m, ___ for x1, and ____ for y1
8. Use distributive property 9. Add ___ to each side.
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Checkpoint: Write an equation in the slope-intercept form of the line that passes through the given points. 1. (5, -‐6), (-‐2, 1) 2. (-‐2, -‐9). (6, -‐3)
