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Do Now Find the value of m. undefined

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**3.7 Equations of lines in a coordinate plane**

Target: SWBAT Find the slope of a line. 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. AB Substitute (–2, 7) for (x1, y1) and (3, 7) for (x2, y2) in the slope formula and then simplify.

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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 (x1, y1) and (4, 2) for (x2, y2) in the slope formula and then simplify.

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**Example 1C: Finding the Slope of a Line**

Use the slope formula to determine the slope of each line. AD Substitute (–2, 7) for (x1, y1) and (–2, 1) for (x2, y2) in the slope formula and then simplify. The slope is undefined.

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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 (x1, y1) and (–2, 1) for (x2, y2) 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 (x1, y1) and (2, –1) for (x2, y2) in the slope formula and then simplify.

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**One interpretation of slope is a rate of change**

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 – y1 = m(x – x1) Point-slope form y – (–4) = 6(x – 3) Substitute 6 for m, 3 for x1, and -4 for y1.

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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 Find the slope. Slope-intercept form y = mx + b 0 = 1(-1) + b Substitute 1 for m, -1 for x, and 0 for y. 1 = b Write in slope-intercept form using m = 1 and b = 1. y = x + 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 Use the point (3,-5) to find the slope. y – y1 = m(x – x1) Point-slope form Substitute for m, 3 for x1, and 0 for y1. 5 3 y – 0 = (x – 3) 5 3 y = (x - 3) 5 3 Simplify.

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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 – y1 = m(x – x1) Point-slope form Substitute 0 for m, 4 for x1, and 6 for y1. y – 6 = 0(x – 4) y = 6

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**Write the equation of each line in the given form.**

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 Find the slope. y – y1 = m(x – x1) Point-slope form Substitute 0 for m, 1 for x1, and 2 for y1. y – 2 = 0(x – 1) y - 2 = 0 Simplify.

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**Example 2A: Graphing Lines**

Graph each line. 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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**Example 2B: Graphing Lines**

Graph each line. 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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**Example 2C: Graphing Lines**

Graph each line. y = –3 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). (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 Foundation – (9-15 odd, even, odd) Core – (38, 39, 45, 47, 56) Challenge - (58)

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Lines in the Coordinate Plane

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