1.4 Linear Functions and Slope The slope of a line passing through the points (x1, y1) and (x2, y2) is found by using the slope formula: Determine the slope of a line passing through each pair of points below. a) (5, 1) and (3, 4) b) (0, 7) and (3, 1) c) (4, 7) and (4, 2) The slope of a line can be positive (line rises to the right), negative (line falls to the right), zero (horizontal line), or undefined (vertical line). 1 The equation of a line can be expressed in slopeintercept form as y = mx + b, in pointslope form as y y1 = m(x x1), or in standard form as Ax + By = C. The equation of a line can be written if we know: a) the slope and yintercept; e.g. m = 2/3, b = 7 b) the slope and a point; e.g. m = 3, point (x1, y1) = (4, 2) c) two points on the line; e.g. (x1, y1) = (3, 7) and (x2, y2) = (1, 1) 2 Examples: 1) Write the equation of a line which passes through the origin and has a slope of 2/3. 2) Write the equation of a line which has xintercept 3 and yintercept 5. 3) Write the equation of a line which has slope 0 and passes through the point (4, 7). 4) Write the equation of a line which passes through the points (4, 1) and (2, 1). 5) Write the equation of a line which passes through the point (3, 5) and has xintercept 7. 3 We can easily graph the equation of a line if we know its slope and yintercept. State the slope and yintercept of each equation and then graph. y = 2x 5 y = x Rewrite each equation in slopeintercept form and then state the slope and yintercept. a) 4x + y 6 = 0 b) 6x 5y 20 = 0 4 The equation of a horizontal line (slope 0) is y = b, where b is the yintercept. The equation of a vertical line (slope undefined) is x = a, where a is the xintercept. Graph each equation on the grid provided. y = 3 x = 2 y = x 5 Determine the xintercept and yintercept of each line whose equation is given, and use these points to graph. 2x 3y = 12 x + y = 5 3x y + 6 = 0 6 7
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