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ALGEBRA 1 Lesson 5-4 Warm-Up

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ALGEBRA 1 “Point-Slope Form and Writing Linear Equations” (5-4) (5-3) What is “point- slope form”? How can you use point-slope form? Point-Slope Form: the equation of a nonvertical (not vertical or straight up and down) line that passes through point (x 1, y 1 ) and which has a slope m is: y – y 1 = m (x – x 1 ) This equation is derived from the definition of slope, or m = after multiplying both sides by (x 2 – x 1 ). You can use point-slope form to find the equation of a line with a given slope that passes through a given number (in other words, you’re only given the slope of the line and one point on the line). Example: What is the equation of a line that passes through (3,4) and has a slope of 2. y 2 – y 1 x 2 – x 1

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ALGEBRA 1 1313 The equation shows that the line passes through (1, 2) with slope. Graph the equation y – 2 = (x – 1). 1313 Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples Start at (1, 2). Using the slope, go up 1 unit and right 3 units to (4, 3). Draw a line through the two points.

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ALGEBRA 1 Simplify the grouping symbols.y + 3 = –2(x – 3) Write the equation of the line with slope –2 that passes through the point (3, –3). y – y 1 = m(x – x 1 ) Substitute (3, –3) for (x 1, y 1 ) and –2 for m. y – (–3) = –2(x – 3) Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples

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ALGEBRA 1 The slope is –. 1313 Step 1 Find the slope. = m y 2 – y 1 x 2 – x 1 4 – 3 –1 – 2 = – 1313 Write equations for the line in point-slope form and in slope-intercept form. Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples

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ALGEBRA 1 (continued) Step 3 Rewrite the equation from Step 2 in slope– intercept form. y – 4 = – (x + 1) y – 4 = – x – y – 4 – 4 = – x – – 4 y = – x + 3 1313 1313 1313 2323 1313 Step 2 Use either point to write the equation in point-slope form. Use (–1, 4). y – y 1 = m(x – x 1 ) y – 4 = – (x – (– 1)) y – 4 = – (x + 1) 1313 1313 Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples 1313 1313

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ALGEBRA 1 “Point-Slope Form and Writing Linear Equations” (5-4) (5-3) How can you tell that two sets of data have a linear relationship? Two sets of data have a linear relationship (form a line on a graph) if the rate of change (“rise” “run”) between consecutive pairs (one pair after the other in order) of data is the same. If the data pairs form a line (linear relationship), the rate of change is the slope of that line. Example: Is the relationship shown in the data table linear? The relationship between the two set of data is linear. The rate of change, or slope, is. 1212

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ALGEBRA 1 Step 1 Find the rate of change for consecutive ordered pairs. –2 –1 –6 –3 –2 –1 = 2 The relationship is linear. The rate of change is 2. Is the relationship shown by the data linear? If so, model the data with an equation. –1( ) –2 –3( ) –6 –2( ) –4 36 2 –1 –3 4 –2 –6 xy Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples

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ALGEBRA 1 y – y 1 = m(x – x 1 ) Use the point-slope form. y – 4 = 2(x – 2)Substitute (2, 4) for (x 1, y 1 ) and 2 for m. Step 2Use the slope and a point to write an equation. (continued) Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples

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ALGEBRA 1 The relationship is not linear. Is the relationship shown by the data linear? If so, model the data with an equation. –1 ( ) –1 –2 ( ) –1 –1 ( ) –1 –2 –1 1 2 0 1 xy Find the rate of change for consecutive ordered pairs. –1 = 1 –1 = 1 –1 –2 / Point-Slope Form and Writing Linear Equations LESSON 5-4 Additional Examples

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ALGEBRA 1 –10–7 0 5 20 –3 –1 5 xy Point-Slope Form and Writing Linear Equations LESSON 5-4 Lesson Quiz 2323 2525 yes; y + 3 = (x – 0) 6565 6565 7575 y + 5 = – (x – 3); y = – x –y – 4 = – (x – 0), or y = – x + 4 2323 2323 1. Graph the equation y + 1 = –(x – 3). 2. Write an equation of the line with slope – that passes through the point (0, 4). 3. Write an equation for the line that passes through (3, –5) and (–2, 1) in point-slope form and slope-intercept form. 4. Is the relationship shown by the data linear? If so, model that data with an equation.

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