
StraightLine Equations: PointSlope Form (page 2 of 3) Sections: Slopeintercept form, Pointslope form, Parallel and perpendicular lines The other format for straightline equations is called the "pointslope" form. For this one, they give you a point (x_{1}, y_{1}) and a slope m, and have you plug it into this formula: y – y_{1} = m(x – x_{1}) Don't let the subscripts scare you. They are just intended to indicate the point they give you. You have the generic "x" and generic "y" that are always in your equation, and then you have the specific x and y from the point they gave you; the specific x and y are what is subscripted in the formula. Here's how you use the pointslope formula:
This is the same line that I found on the previous page, so I already know what the answer is (namely, y = 4x – 2). But let's see how the process works with the pointslope formula. They've given me m = 4, x_{1} = –1, and y_{1} = –6. I'll plug these values into the pointslope form, and solve for "y=": y – y_{1} = m(x – x_{1}) y = 4x – 2 Copyright © Elizabeth Stapel 20002011 All Rights Reserved This matches the result I got when I plugged into the slopeintercept form. This shows that it really doesn't matter which method you use (unless the text or teacher specifies). You can get the same answer either way, so use whichever method works more comfortably for you. You can use the Mathway widget below to practice finding a line equation using the pointslope formula. Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)
(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free sevenday trial of the software.) You can find the straightline equation using the pointslope form if they just give you a couple points:
I've already answered this one, but let's look at the process. I should get the same result (namely, y = ( –^{ 2}/_{3 }) x + ^{8}/_{3 }). Given two points, I can always find the slope: Then I can use either point as my (x_{1}, y_{1}), along with this slope Ive just calculated, and plug in to the pointslope form. Using (–2, 4) as the (x_{1}, y_{1}), I get:
y – y_{1} = m(x – x_{1}) y = ( –^{ 2}/_{3 }) x + ^{8}/_{3} This is the same answer I got when I plugged into
the slopeintercept form. So, unless your text or teacher specifies the method or format to use,
you should use whichever format suits your taste, because you'll get the same answer either way. You can use the Mathway widget below to practice finding a line equation from two points. Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)
(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free sevenday trial of the software.) In the examples in the next section, I'll use the pointslope formula, because that's the way I was taught and that's what most books want. But my experience has been that most students prefer to plug the slope and a point into the slopeintercept form of the line, and solve for b. If that works better for you, use that method instead. << Previous Top  1  2  3  Return to Index Next >>


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