The equation is useful when we know:
and want to find other points on the line. Have a play with it (move the point, try different slopes): Now let's discover more. What does it stand for?(x1, y1) is a known point m is the slope of the line (x, y) is any other point on the line It is based on the slope: Slope m = change in y change in x = y − y1 x − x1
So, it is just the slope formula in a different way! Now let us see how to use it.
slope "m" = 31 = 3 y − y1 = m(x − x1) We know m, and also know that (x1, y1) = (3, 2), and so we have: That is a perfectly good answer, but we can simplify it a little: y − 2 = 3x − 9 y = 3x − 9 + 2 y = 3x − 7
m = −3 1 = −3 y − y1 = m(x − x1) We can pick any point for (x1, y1), so let's choose (0,0), and we have: y − 0 = −3(x − 0) Which can be simplified to:
What is the equation for a vertical line? In fact, this is a special case, and we use a different equation, like this: Every point on the line has x coordinate 1.5, What About y = mx + b ?You may already be familiar with the y=mx+b form (called the slope-intercept form of the equation of a line). It is the same equation, in a different form! The "b" value (called the y-intercept) is where the line crosses the y-axis. So point (x1, y1) is actually (0, b) and the equation becomes:
Start withy − y1 = m(x − x1) (x1, y1) is (0, b):y − b = m(x − 0) Which is:y − b = mx Put b on other side:y = mx + b 519, 521, 522, 1160, 1161, 1162, 2074, 2075, 9027, 9028, 9029 Copyright © 2022 Rod Pierce |