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When we are given two points, we can use the slope formula to find the slope of the line between them. Example: You are given the points (4, 7) and (2, 6). Find the slope. m = rise = y 2 – y 1 = 6 – 7 = 1 run x 2 – x 1 2 – 4 2

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Step 1: Find the slope. Substitute the coordinates of the two given points into the formula for slope, m = y 2 – y 1 x 2 – x 1 Step 2: Find the y-intercept. Substitute the slope m and the coordinates of one of the points into the slope-intercept form, y = mx +b, and solve for the y-intercept. Step 3: Write an equation of the line. Substitute the slope m and the y-intercept b into the slope-intercept form, y = mx + b.

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Write an of a line that passes through the points (3, 5) and (4, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 7 – 5 = 2 = 2 x 2 – x 1 4 – 3 1 Now we must find the y-intercept. y = mx + b 5 = 2(3) + b 5 = 6 + bSubtract 6 from both sides. -1 = b Now let’s write the equation of the line. y = mx + b y = 2x – 1

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Write an equation of a line that passes through the points (9, 4) and (8, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 7 – 4 = 3 = -3 x 2 – x 1 8 – 9 -1 Now we must find the y-intercept. y = mx + b 4 = -3(9) + b 4 = -27 + bAdd 27 to both sides. 31 = b Now let’s write the equation of the line. y = mx + b y = -3x + 31

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Write an equation of a line that passes through the points (6, 1) and (2, 4). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 4 – 1 = 3 x 2 – x 1 2 – 6 -4 Now we must find the y-intercept. y = mx + b 1 = (-3/4)(6) + b 1 = -4.5 + bAdd 4.5 to both sides. 5.5 = b Now let’s write the equation of the line. y = mx + b y = (-3/4)x + 5.5

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Two different nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. For example: The negative reciprocal of 4 is: -1/4 The negative reciprocal of -3 is: 1/3 The negative reciprocal of -2/3 is: 3/2 The negative reciprocal of 7/2 is: -2/7

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Using the figure to the left, show that two of the lines are perpendicular. The slope of AB: m = 7 – 1 = 6 = 3 -4 + 8 4 2 The slope of BC: m = 1 + 7 = 8 = 2 -8 -4 -12 -3 Notice that these two lines have slopes that are negative reciprocals of each other. This means that they are perpendicular. A (-4, 7) B (-8, 1) C (4, -7) D (8, -1)

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Write an equation of a line that is perpendicular to y = 6x – 3 and passes through the point (4, 5). y = mx + b 5 = (-1/6)(4) + b 5 = -2/3 + b 17/3 = b y = (-1/6)x + 17/3 Write an equation of a line that is perpendicular to y = (1/2)x + 3 and passes through the point (1, 4). y = mx + b 4 = -2(1) + b 4 = -2 + b 6 = b y = -2x + 6

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Linear Functions Slope and y = mx + b. Remember Slope… Slope is represented by m m = 0 Horizontal Line Vertical Line Slope up to the right Slope up to.

Linear Functions Slope and y = mx + b. Remember Slope… Slope is represented by m m = 0 Horizontal Line Vertical Line Slope up to the right Slope up to.

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