New SAT Math Workbook

Notice that line p slopes downward from left to right

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Unformatted text preview: subtract x2 from x1. In the xy-plane: • A line sloping upward from left to right has a positive slope (m). A line with a slope of 1 slopes upward from left to right at a 45° angle in relation to the x-axis. A line with a fractional slope between 0 and 1 slopes upward from left to right but at less than a 45° angle in relation to the x-axis. A line with a slope greater than 1 slopes upward from left to right at more than a 45° angle in relation to the x-axis. • A line sloping downward from left to right has a negative slope (m). A line with a slope of –1 slopes downward from left to right at a 45° angle in relation to the x-axis. A line with a fractional slope between 0 and –1 slopes downward from left to right but at less than a 45° angle in relation to the x-axis. A line with a slope less than –1 (for example, –2) slopes downward from left to right at more than a 45° angle in relation to the x-axis. • A horizontal line has a slope of zero (m = 0, and mx = 0) • A vertical line has either an undefined or an indeterminate slope (the fraction’s denominator is 0), so the mterm in the equation is ignored. • Parallel lines have the same slope (the same m-term in the general equation). • The slope of a line perpendicular to another is the negative reciprocal of the other line’s slope. (The product 3 of the two slopes is 1.) For example, a line with slope 2 is perpendicular to a line with slope − 2 . 3 On the new SAT, a question involving the equation or graph of a line might ask you to apply one or more of the preceding rules in order to perform tasks such as: • Identifying the slope of a line defined by a given equation (in which case you simply put the equation in the standard form y = mx + b, then identify the m-term. • Determining the equation of a line, or just the line’s slope (m) or y-intercept (b), given the coordinates of two points on the line. • Determining the point at which two non-parallel lines intersect on the coordinate plane (in which case you determine the equation for each line, and then solve for x and y by either substitution or addition-subtraction) • Recognizing the slope or t...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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