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1 Topic The Slope-Intercept Form of a Line The Slope-Intercept Form of a Line

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2 The Slope-Intercept Form of a Line California Standard: 8.0 Students understand the concepts of parallel lines and perpendicular lines and how their slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. What it means for you: You’ll plot graphs and solve equations using a method called the slope-intercept form of an equation. Key Words: slope-intercept form intercept Topic 4.4.3

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3 The Slope-Intercept Form of a Line Now that you’ve practiced calculating the slope and intercept of a line, you can use the two things together to make plotting graphs easier. Topic –6–4– y x –4 –6

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4 The Slope-Intercept Form of a Line The Slope-Intercept Form of a Line: y = mx + b In the slope-intercept form the y is alone on one side of the equation. Topic Here are a few examples of equations in the slope-intercept form: The slope-intercept form of the equation is: y = mx + b y = 3 x + 2 y = – x + 1 y = – x + 1 y = x –

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5 The Slope-Intercept Form of a Line Guided Practice In Exercises 1–6, decide whether each equation is in slope-intercept form or not. Topic y = 3 x x + 4 y = 7 3. y – 3 = 2( x – 4)4. y – 8 = 3( x – 4) 5. y = x y = –4 x – 1 Solution follows… 3 2 yes no yes no yes no

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6 The Slope-Intercept Form of a Line The Slope-Intercept Form Makes It Easy to Plot Graphs The slope-intercept form of an equation is really useful for plotting graphs because m is the slope of the line and b is the y -coordinate of the y -intercept. Topic y = mx + by = mx + b y -coordinate of y -intercept slope

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7 The Slope-Intercept Form of a Line Example 1 Plot the graph of y = x + 2. Solution follows… Solution Topic y = mx + b = x — for a slope of, go up 1 unit for every 2 units across. Slope = m = y -coordinate of the y -intercept = b = 2 — so the y -intercept is (0, 2). 1 2 –6–4– y x –4 –6 y = x

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8 The Slope-Intercept Form of a Line Example 2 Plot the graph of y = –3 x – 4. Solution follows… Solution Topic y = mx + b = –3 x – 4 Slope = m = –3 — for a slope of –3, go down 3 units for every unit across. y -coordinate of the y -intercept = b = –4 — so the y-intercept is (0, –4). –6–4– y x –4 –6 y = –3 x – 4

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9 The Slope-Intercept Form of a Line Guided Practice 7. In the equation y = 8 x + 5, find the slope. 8. In the equation y = – x + 10, find the slope. 9. In the equation y = 2 x + 5, find the y -intercept. 10. In the equation y = 7 b – 3, find the y -intercept. Topic Solution follows… y -intercept = (0, 5) m = 8 m = –1 y -intercept = (0, –3)

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10 The Slope-Intercept Form of a Line Guided Practice In Exercises 11–14, plot each equation on a graph. Topic Solution follows… 11. y = 2 x y = x – y = –7 x – y = – x – –6–4– y x –4 –6 –8

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11 The Slope-Intercept Form of a Line Guided Practice In Exercises 15–18, plot each equation on a graph. Topic y = – x y = x – y = x 18. y = Solution follows…

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12 The Slope-Intercept Form of a Line Solve for y to Get the Slope-Intercept Form OK, so you know the slope-intercept form of an equation makes drawing graphs a lot easier. Topic To get the equation into slope-intercept form, solve for y. The trouble is, you’ll often be given an equation which isn’t in slope-intercept form.

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13 The Slope-Intercept Form of a Line Example 3 A line has the equation Ax + By = C, where B 0. Solve this equation for y, justifying each step. Solution follows… Solution Topic Ax + By = C Ax – Ax + By = – Ax + C Given equation Subtraction property of equality By = – Ax + C Solution continues… Division property of equality

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14 The Slope-Intercept Form of a Line Example 3 A line has the equation Ax + By = C, where B 0. Solve this equation for y, justifying each step. Solution (continued) Topic The equation is now in slope-intercept form. The slope, m = – and the y -coordinate of the y -intercept, b = –. A B C B

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15 The Slope-Intercept Form of a Line Example 4 Determine the slope and y -intercept of the line 2 x – 3 y = 9. Solution follows… Solution Topic Step 1: Solve the given equation for y. 2 x – 3 y = 9 –3 y = –2 x + 9 y = x – y = Now you’ve got the equation in slope-intercept form, y = mx + b. Solution continues…

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16 The Slope-Intercept Form of a Line Example 4 Determine the slope and y -intercept of the line 2 x – 3 y = 9. Solution (continued) Topic Step 2: Get the slope and y -intercept from the equation. The slope, m =. 2 3 The y -coordinate of the y -intercept, b = –3. So, the y -intercept = (0, –3). y = x – Step 1:

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17 The Slope-Intercept Form of a Line Guided Practice In Exercises 19-24, find the slope and y -intercept of the line. Topic x + 3 y = y – 6 x = x – 2 y = –7 y + 5 x = –2 y + 3 x = –5 x + 4 y = 12 Solution follows… m = –1, (0, 3) x + y = 3 y = – x + 3 m = 3, (0, 5) y – 3 x = 5 y = 3 x + 5 m = 1, (0, – ) 5 2 x – y = y = x – m =, (0, –2) 5 7 y – x = –2 y = x – m =, (0, –4) 3 2 y – x = –4 y = x – m =, (0, 3) 5 4 – x + y = 3 y = x

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18 The Slope-Intercept Form of a Line Guided Practice Write down the equations of the following lines in slope-intercept form. Topic The line with slope 4 that passes through the point (0, 2). 26. The line with slope 2 that passes through the point (0, –6). 27. The line with slope –3 that passes through the point (0, 1). Solution follows… y = 4 x + 2 y = –3 x + 1 y = 2 x – The line with slope – that passes through the point (0, –3). 6 7 y = – x – 3

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19 Independent Practice Solution follows… The Slope-Intercept Form of a Line Topic In Exercises 1–10, find the slope and y -intercept of each equation that’s given. 3. y = 3 x –6 y = 3 x y = 2( x + 2) 6. y – 4 = 2( x + 1) 7. 7 – y = 5( x + 4) 8. y – 3 = 2( x – 9) 9. 3 x + 4 y = x + 3 y = 9 1. y = x – 5 2. y = x m = 3, (0, 6) m = 2, (0, 4) m = 2, (0, 6) m = –5, (0, –13) m = 2, (0, –15) 3 4 m = –, (0, 2) m =, (0, –5) 1 2 m = –, (0, 3) 2 3 m =, (0, 1) 2 3 m = –, (0, –2) 1 2

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20 Independent Practice Solution follows… The Slope-Intercept Form of a Line Topic In Exercises 11–15, plot the graph of the given equation. 11. y = x y = – x – y = x y = – x y = 2 x

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21 Independent Practice Solution follows… The Slope-Intercept Form of a Line Topic In Exercises 16–20, write the equations of the lines in slope-intercept form. 16. A line with slope that passes through the point (0, 4). 17. A line with slope that passes through the point (0, –2) x + 2 y = x – 3 y = x – 4 y = –16 y = –2 x + 4 y = 2 x – 5 y = x y = x – 2 1 2

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22 Independent Practice Solution follows… The Slope-Intercept Form of a Line Topic In Exercises 21–22, write the equations of the lines in slope-intercept form. 21. The line with slope 0 that passes through the point (2, 6) 22. The line with slope 2 that passes through the point (6, 3) y = 6 y = 2 x – 9

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23 Round Up If m = 0, the slope-intercept form of the equation becomes y = b — the equation of a horizontal line. If b = 0, the equation becomes y = mx, meaning the line passes through the origin. The Slope-Intercept Form of a Line Topic 4.4.3

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