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$slope intercept form calculator equation$

If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. (Notice that the subscript ⊥ ⊥ looks like the right angles made by two perpendicular lines.) We’ll use the notation m ⊥ m ⊥ to represent the slope of a line perpendicular to a line with slope m. We know that perpendicular lines have slopes that are negative reciprocals. Now, we want to graph a line perpendicular to this line and passing through ( −2, 1 ). We will again use the point-slope equation, like we did with parallel lines. We can use the fact that perpendicular lines have slopes that are negative reciprocals. Suppose we need to find a line passing through a specific point and which is perpendicular to a given line.

Write the equation in slope-intercept form.įind an Equation of a Line Perpendicular to a Given Line Substitute the values into the point-slope form: y − y 1 = m ( x − x 1 ). So we will use the point-slope form.įind an equation of a line parallel to a given line. Here we know one point and can find the slope. We can use either the slope-intercept form or the point-slope form to find an equation of a line. We were asked to graph the line, now let’s see how to do this algebraically. We draw the line, as shown in the graph.ĭo the lines appear parallel? Does the second line pass through ( −2, 1 ) ? ( −2, 1 ) ? With m = 2 m = 2 (or m = 2 1 m = 2 1), we count out the rise 2 and the run 1. To graph the line, we start at ( −2, 1 ) ( −2, 1 ) and count out the rise and run. The second line will pass through ( −2, 1 ) ( −2, 1 ) and have m = 2. (Notice that the subscript || looks like two parallel lines.) We’ll use the notation m ∥ m ∥ to represent the slope of a line parallel to a line with slope m. So the second line will have the same slope as y = 2 x − 3. We know that parallel lines have the same slope. We want to graph a line parallel to this line and passing through the point ( −2, 1 ). So we will have a point and the slope-just what we need to use the point-slope equation. We can use the fact that parallel lines have the same slope. Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. Y − y 1 = m ( x − x 1 ) y − y 1 = m ( x − x 1 )įind an Equation of a Line Parallel to a Given Line Now we will do the reverse-we will start with the slope and y-intercept and use them to find the equation of the line. We can easily determine the slope and intercept of a line if the equation is written in slope-intercept form, y = m x + b. Find an Equation of the Line Given the Slope and y-Intercept The specific method we use will be determined by what information we are given. In this section, we will look at several ways to write the equation of a line.

To create a mathematical model of a linear relation between two variables, we must be able to find the equation of the line. The physical sciences, social sciences, and the business world are full of situations that can be modeled with linear equations relating two variables. How do online companies know that “you may also like” a particular item based on something you just ordered? How can economists know how a rise in the minimum wage will affect the unemployment rate? How do medical researchers create drugs to target cancer cells? How can traffic engineers predict the effect on your commuting time of an increase or decrease in gas prices? It’s all mathematics. If you missed this problem, review Example 2.31.

Slope intercept form calculator equation