Explanation : For two lines to be perpendicular they have to have slopes that multiply to get. Explanation : If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line. Copyright Notice. Francisco Certified Tutor. University of Texas at Brownsville, Bachelors, Mathematics. University of Texas at Brownsville, Masters, Mathematics.
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Top Subjects. Our Company. Varsity Tutors. How To: Given the equation of a linear function, write the equation of a line WHICH passes through a given point and is parallel to the given line. Find the slope of the function. Substitute the slope and given point into point-slope or slope-intercept form. Show Solution The slope of the given line is 3. Analysis of the Solution We can confirm that the two lines are parallel by graphing them. How To: Given the equation of a linear function, write the equation of a line WHICH passes through a given point and is Perpendicular to the given line.
Find the slope of the given function. Determine the negative reciprocal of the slope. Solve for b. Write the equation of the line. Analysis of the Solution A graph of the two lines is shown below. How To: Given two points on a line and a third point, write the equation of the perpendicular line that passes through the point. Determine the slope of the line passing through the points. Find the negative reciprocal of the slope. Use slope-intercept form or point-slope form to write the equation by substituting the known values.
Example: Finding the Equation of a Line going through a point and Perpendicular to a Given Line A line passes through the points —2, 6 and 4, 5. Show Solution From the two points of the given line, we can calculate the slope of that line. Try It A line passes through the points, —2, —15 and 2, —3. Did you have an idea for improving this content? Licenses and Attributions. CC licensed content, Original.
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Post as a guest Name. The two lines in Figure 18 are parallel lines : they will never intersect. Notice that they have exactly the same steepness, which means their slopes are identical. The only difference between the two lines is the y -intercept. If we shifted one line vertically toward the y -intercept of the other, they would become the same line. We can determine from their equations whether two lines are parallel by comparing their slopes.
If the slopes are the same and the y -intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel.
Unlike parallel lines, perpendicular lines do intersect. Their intersection forms a right, or degree, angle.
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