The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point <span>(x1, y1)</span><span> and a slope </span>m, and have you plug it into this formula:
<span><span>y </span>–<span> y</span>1<span> = m</span>(<span>x </span>–<span> x</span>1)</span>
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<span>" that are always in your equation, and then you have the specific </span>x<span> and </span>y<span> from the point they gave you; the specific </span>x<span> and </span>y<span> are what is subscripted in the formula. Here's how you use the point-slope formula:</span>
<span><span>Find the equation of the straight line that has slope </span><span>m = 4</span><span> and passes through
the point </span>(–1, –6).</span><span><span>This is the same line that I found on the </span>previous page<span>, so I already know what the answer is (namely, </span><span>y = 4x – 2</span>). But let's see how the process works with the point-slope formula.<span>They've given me </span><span>m = 4, x1 = –1,</span><span> and </span><span>y1 = –6</span>. I'll plug these values into the point-slope form, and solve for "<span>y=</span>":<span><span><span>y </span>–<span> y</span>1 = m(<span>x </span>–<span> x</span>1)
y – (–6) = (4)(x – (–1))
y + 6 = 4(x + 1)
y + 6 = 4x + 4
y = 4x + 4 – 6</span><span>y = 4x – 2</span> Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved</span></span>
This matches the result I got when I plugged into the slope-intercept 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.
<span>You can use the Mathway widget below to practice finding a line equation using the point-slope 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.)</span>
