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Unformatted text preview: Section 2.3 Lines Objective 1 : Determining the Slope of a Line In mathematics, the steepness of a line can be measured by computing the lines slope. Every non-vertical line has slope. Vertical lines are said to have no slope. A line going up from left to right has positive slope , a line going down from left to right has negative slope, while a horizontal line has zero slope . We use the variable m to describe slope. Slope = m The slope can be computed by comparing the vertical change (the rise) to the horizontal change (the run ). Given any two points on the line, the slope m can be computed by taking the quotient of the rise over the run. Definition of Slope If 1 2 x x , the slope of a line passing through distinct points ( 29 1 1 , x y and ( 29 2 2 , x y is 2 1 2 1 y y rise Changein y m run Changein x x x- = = =- Objective 2 : Sketching a Line Given a Point and the Slope If we know a point on a line and the slope, we can quickly sketch the line. Objective 3 : Finding the Equation of a Line Using the Point-Slope Form Given the slope m of a line and a point on the line, ( 29 1 1 , x y , we can use what is known as the point-slope form of the equation to determine the equation of the line. The Point-Slope Form of the Equation of a Line Given the slope of a line m and a point on the line ( 29 1 1 , x y , the point-slope form of the equation of a line is given by ( 29 1 1 y y m x x- =- . Objective 4...
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