Section 3.5 Writing Equations of Lines 251 ���������������������� Writing the Equation of a Line Given a Point and a Slope Method 1: Use the slope-intercept form of a line Step 1: In the equation y = mx + b, substitute the given point (x, y) for the x-value and the y-value in the equation. Substitute the slope for m. Step 2: Solve the resulting equation for b. Step 3: Write the equation in the form y = mx + b by substituting the given slope and the value of b. Step 4: Check the equation. Method 2: Use the point-slope form of a line Step 1: In the equation y - y1 = m(x - x1), substitute the given point (x1, y1) and the slope for m. Step 2: Simplify both sides of the equation. Step 3: Write the equation in either standard form or slopeintercept form. Step 4: Check the equation. �� ������������������������ ������������������ Write the equation of the line that has the given slope and passes through the given point. Write the answer in both slope-intercept form and standard form. 2a. m = 3; (5, -2) 2b. m=- 3 4 ; (1, 5) 2c. m = 0; (-2, 1) 2d. undefined slope; (-3, 9) Solutions 2a. Method 1 m = 3 and (x, y) = (5, -2) y = mx + b -2 = 3(5) + b -2 = 15 + b -2 - 15 = 15 + b - 15 -17 = b Equation in standard form: y = 3x - 17 Begin with the slope-intercept form. y - 3x = 3x - 17 - 3x Subtract 3x from each side. -3x + y = -17 Simplify. -1(-3x + y) = -1(-17) Multiply each side by -1. 3x - y = 17 Simplify. Check: Show that (5, -2) is a solution of y = 3x - 17 or 3x - y = 17. y = 3x - 17 Begin with the slope-intercept form. -2 = 3(5) - 17 Let x = 5 and y = -2. -2 = 15 - 17 Simplify. -2 = -2 Simplify. Since the resulting equation is true, our work is correct. Method 2 m = 3 and (x1, y1) = (5, -2) y - y1 = m(x - x1) y - (-2) = 3(x - 5) y + 2 = 3x - 15 y + 2 - 2 = 3x - 15 - 2 y = 3x - 17 Equation in slope-intercept form: y = 3x - 17 Equation in slope-intercept form: y = 3x - 17
hendricks_beginning_algebra_1e_ch1_3
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