Section 3.5 Writing Equations of Lines 255 Since the slope is undefined, the line is vertical. Recall that a vertical line is represented by an equation of the form x = h, where h is the x-coordinate of a point on the line. Since the given points are (-2, 4) and (-2, 11), h = -2. So, the equation of the line is x =-2. Student Check 3 Write the equation of the line, in slope-intercept form, that passes through the given points. a. (3, -7) and (1, 3) b. (-1, 2) and (5, -6) c. (4, -1) and (6, -1) Use a Point and a Line to Write the Equation of a Line The last case we will discuss is writing the equation of a line given a point and a relationship to another line. We will be given the equation of a parallel or perpendicular line. Knowing this information enables us to find the slope of the unknown line. If the lines are parallel, the slopes are the same. If the lines are perpendicular, the slopes are negative reciprocals. Once the slope is determined, the methods to find the equation of a line, as previously stated, apply. ���������������������� Writing the Equation of a Line Given a Point and a Relationship to Another Line Step 1: Determine the slope of the given line by writing the equation in slopeintercept form. Step 2: Determine the slope of the unknown line. a. The slope will be the same as the given line if the lines are parallel. b. The slope will be the negative reciprocal of the given line if the lines are perpendicular. Step 3: Use the slope from step 2 and the given point to write the equation of the unknown line using either method 1 or method 2. �� ������������������������ ������������������ Write the equation of the line that passes through the given point and is either parallel or perpendicular to the given line. 4a. (1, -5) and parallel to 4x - y = 8; Write answer in slope-intercept form. 4b. (-2, 4) and perpendicular to y = 5x - 6; Write answer in standard form. 4c. (-2, 3) and parallel to x = 5 4d. (4, -7) and perpendicular to x =5 Solutions 4a. We first find the slope of 4x - y = 8 by writing it in slope-intercept form. 4x - y = 8 4x - y - 4x = 8 - 4x -y = -4x + 8 -1(-y) = -1(-4x + 8) y = 4x - 8 The slope of the line 4x - y = 8 is m = 4. Since the lines are parallel, the slope of the unknown line is also m = 4. Now we find the equation of the line with slope m = 4 that passes through (1, -5). y - y1 = m(x -x1) y - (-5) = 4(x -1) y + 5 = 4x - 4 y + 5 - 5 = 4x - 4 - 5 y = 4x - 9 So, the equation of the line through (1, -5) and parallel to 4x- y = 8 is y = 4x - 9. Objective 4 ▶ Write the equation of a line given a point and a relationship to another line. Subtract 4x from each side. Simplify. Multiply each side by -1. Simplify. State the point-slope form. Let m = 4, (x1, y1) = (1, -5). Simplify and distribute. Subtract 5 from each side. Simplify.
hendricks_beginning_algebra_1e_ch1_3
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