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Do Now Find the value of m. 1.2. 3.4. undefined0

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Target: SWBAT Find the slope of a line. 3.7 Equations of lines in a coordinate plane Target: SWBAT Graph lines and write their equations in slope-intercept and point-slope form.

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The slope of a line in a coordinate plane is a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.

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Example 1A: Finding the Slope of a Line Use the slope formula to determine the slope of the line. Substitute (–2, 7) for (x 1, y 1 ) and (3, 7) for (x 2, y 2 ) in the slope formula and then simplify. AB

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Example 1B: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AC Substitute (–2, 7) for (x 1, y 1 ) and (4, 2) for (x 2, y 2 ) in the slope formula and then simplify.

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The slope is undefined. Example 1C: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AD Substitute (–2, 7) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

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A fraction with zero in the denominator is undefined because it is impossible to divide by zero. Remember!

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Example 1D: Finding the Slope of a Line Use the slope formula to determine the slope of each line. CD Substitute (4, 2) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

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Check It Out! Example 1 Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1). Substitute (3, 1) for (x 1, y 1 ) and (2, –1) for (x 2, y 2 ) in the slope formula and then simplify.

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One interpretation of slope is a rate of change. If y represents miles traveled and x represents time in hours, the slope gives the rate of change in miles per hour.

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Example 1A: Writing Equations In Lines Write the equation of each line in the given form. the line with slope 6 through (3, –4) in point- slope form y – y 1 = m(x – x 1 ) y – (–4) = 6(x – 3) Point-slope form Substitute 6 for m, 3 for x 1, and -4 for y 1.

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Example 1B: Writing Equations In Lines Write the equation of each line in the given form. the line through (–1, 0) and (1, 2) in slope- intercept form y = mx + b 0 = 1(-1) + b 1 = b y = x + 1 Slope-intercept form Find the slope. Substitute 1 for m, -1 for x, and 0 for y. Write in slope-intercept form using m = 1 and b = 1.

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Example 1C: Writing Equations In Lines Write the equation of each line in the given form. the line with the x-intercept 3 and y-intercept –5 in point slope form y – y 1 = m(x – x 1 ) Point-slope form Use the point (3,-5) to find the slope. Simplify. Substitute for m, 3 for x 1, and 0 for y 1. 5 3 y = (x - 3) 5 3 y – 0 = (x – 3) 5 3

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Check It Out! Example 1a Write the equation of each line in the given form. the line with slope 0 through (4, 6) in slope- intercept form y = 6 y – y 1 = m(x – x 1 ) y – 6 = 0(x – 4) Point-slope form Substitute 0 for m, 4 for x 1, and 6 for y 1.

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Check It Out! Example 1b Write the equation of each line in the given form. the line through (–3, 2) and (1, 2) in point- slope form y - 2 = 0 Find the slope. y – y 1 = m(x – x 1 ) Point-slope form Simplify. Substitute 0 for m, 1 for x 1, and 2 for y 1. y – 2 = 0(x – 1)

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Graph each line. Example 2A: Graphing Lines 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. (0, 1) rise 1 run 2

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Graph each line. Example 2B: Graphing Lines y – 3 = –2(x + 4) 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. (–4, 3) rise –2 run 1

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Graph each line. Example 2C: Graphing Lines 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). y = –3 (0, –3)

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Check It Out! Example 2a Graph each line. y = 2x – 3 The equation is given in the slope-intercept form, with a slope of and a y-intercept of –3. Plot the point (0, –3) and then rise 2 and run 1 to find another point. Draw the line containing the points. (0, –3) rise 2 run 1

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Check It Out! Example 2b Graph each line. The equation is given in the point-slope form, with a slope of through the point (–2, 1). Plot the point (–2, 1)and then rise –2 and run 3 to find another point. Draw the line containing the points. (–2, 1) run 3 rise –2

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Check It Out! Example 2c 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). (0, –4)

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Assignment #29 - Pages 194-196 Foundation – (9-15 odd, 16-22 even, 25-31 odd) Core – (38, 39, 45, 47, 56) Challenge - (58)

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