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• If the slope is positive, the line rises to the right. • If the slope is negative, the line falls to the right. • If the slope is zero, the line is a horizontal line. • If the slope is undefined, the line is a vertical line. (This occurs when x x 2 1− = 0.) Example 1: Find the slope of each line shown below. A. B. C.
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Definition of Slope. The slope of the line through the distinct points (x 1, y 1) and (x 2, y. Change in y Rise. = Change in x Run. where x – x = 0. 1 2. = y2 – y1. x2 – x1. Rise. y2 – y Run. x1 x2. 2) is . x. y2 x2 – x1. (x2, y2) y1 (x1, y1) y1. Sample Problems: Find the slope of the line thru the points given: (-3,-1) (-3,4) and (-2,4)
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2. Example, find the slope of the line with points ( 2 , 3 ) and ( -7 , 8 ). Use both formulas to verify you get the same slope. = 1 2 x x - 1 y 2 y - = 8 - 3. 5. = -9. -7 - 2. - y. 3 - 8 2 1 x x - = 2 - -7. = -5. 9. 5. = - 9. 5. = - 9. Slope-Intercept Form of an Equation. y = m x + b.
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The following examples show graphs that we find the slope of using this idea. Example 1. Rise -4 Run 6. To find the slope of this line we will consider the rise, or vertical change and the run or horizontal change. Drawing these lines in makes a slope triangle that we can use to count from one point to the next the graph goes down 4, right 6.
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Mar 10, 2024 · Example \(\PageIndex{4}\) What is the slope of the line on the geoboard shown? Solution. Use the definition of slope: \(m = \frac{\text{rise}}{\text{run}}\). Start at the left peg and count the units down and to the right to reach the second peg.
Example 1: Put 3x + y = 7 into slope-intercept form. 3x – 3x + y = – 3x + 7 -subtract 3x from both sides y = –3x + 7 -slope-intercept form Example 2: Put 4x + 2y = 8 into slope intercept form. 4x – 4x + 2y = –4x + 8 -subtract 4x from both sides 2y = –4x + 8 -divide all terms by 2 24 22 8 2 yx− =+ y = –2x + 4 -slope-intercept form.
INTRODUCTION TO SLOPE. Summary (Ready) We will count distances and use slope definitions to find slopes of line segments on a grid and on a set of coordinate axes. We will explore the meaning of positive and negative slopes. Write four equivalent fractions for. 3. Include. 4. denominator. _______ _______ . Write four equivalent fractions for -