Download Goal: Use the slope intercept form to write an

Chapter 5/ Algebra Name: 1 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 yintercept 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 yintercept 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. Chapter 5/ Algebra Name: 2 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 Chapter 5/ Algebra Name: 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. 3 Chapter 5/ Algebra Name: 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. 4 Chapter 5/ Algebra Name: 5 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. Chapter 5/ Algebra Name: 6 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 Chapter 5/ Algebra Name: 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) 7 Chapter 5/ Algebra Name: 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. 8 Chapter 5/ Algebra Name: 9 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. Chapter 5/ Algebra Name: 10 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.
Chapter 5/ Algebra Name: 11 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. Chapter 5/ Algebra Name: 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. 12 Chapter 5/ Algebra Name: 13 Checkpoint: Write an equation in the slopeintercept form of the line that passes through the
given points.
1. (5, -­‐6), (-­‐2, 1) 2. (-­‐2, -­‐9). (6, -­‐3)