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Math 1021 Section 2.3

# Math 1021 Section 2.3 - Point-Slope Form of the Equation of...

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Math 1021 Section 2.3 Lines A linear equation is one in which the variables are raised to the first power. The graph of a linear equation is a line. Slope a measurement of the steepness of a line which is calculated by comparing its vertical change (rise) to its horizontal change (run) Slope of a line, m = rise run 2 1 2 1 y y m x x - = - , x 1 x 2 If x 1 = x 2 , then the line is vertical and the slope is undefined . If slope is positive the line rises from left to right; if the slope is negative the line falls from left to right; if the slope is zero the line is horizontal; and if the slope is undefined the line is vertical. Equation of a Vertical Line: If a line goes through point (a, y) and is vertical, then the equation is given by x = a . Slope is undefined. Equation of a Horizontal Line: If a line goes through point (x, b) and is horizontal, then the equation is given by y = b. Slope is zero.

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Unformatted text preview: Point-Slope Form of the Equation of a Line: y - y 1 = m(x - x 1 ) Given a point (x 1 ,y 1 ) and the slope m on a line. Slope-Intercept Form : y = mx + b ; m = slope and b = y-intercept Standard Form : Ax + By = C , where A, B , and C are real numbers and A and B are not both zero. (X1,Y1) (X2, Y2) rise = y2 - y1 run = x2 - x1 Ex. 1: Given a line containing the point (1, 3) and slope = -2/5, find the equation of the line in slope-intercept form, then graph the line. Ex. 2: Write the equation of the line containing the points (-2, 2) and (1, 4). Express your answer in point-slope form and standard form. Ex. 3: Write the equation of the line given the following properties. a) slope undefined through point (3, -5). b) horizontal line through point (-2, 4). Ex. 4: Find slope and y-intercept of 4x + 5y = -10, then graph the line....
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