Point slope will tell you two things by looking at the equation and doing no work a point on the line, and the slope of the line. Slope - intercept will tell you two things also, the y- intercept if it has one , and the slope. What are the 3 slope formulas? There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. What is the purpose of point slope form?
It's derived from the equation for finding the slope of a line and has practical uses in many areas of mathematics and the real world. How do you solve a slope equation? Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
Find the y-intercept. This can be done by substituting the slope and the coordinates of a point x, y on the line in the slope-intercept formula and then solve for b. How do you find the slope intercept form of an equation? To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form 0, b.
The y- coordinate is the value of b in the equation. Summary Converting Among Forms. Page 1 Page 2. Converting Among Forms The goal in converting an equation to slope-intercept form is to isolate y on one side of the equation. Take a Study Break. We know that the slope between any two points on this line is going to be negative four. So if we take an arbitrary Y that sits on this line and if we find the difference between that Y and, let's focus on this point up here.
So if we find the difference between that Y and this Y, and nine, and it's over the difference between some X on the line and this X, and four. This is going to be the slope between any XY on this line and this point right over here.
And the slope between any two points on a line are going to have to be constant. So this is going to be equal to the slope of the line. It's going to be equal to negative four. And we're not in point-slope form or classic point-slope form just yet. To do that, we just multiply both sides times X minus four. So we get Y minus 9, we get Y minus nine is equal to our slope, negative four times X minus four. Time X minus four. And this right over here is our classic, this right over here is our classic point-slope form.
We have the point, sometimes they even put parenthesis like this, but we could figure out the point from this point-slope form. The point that sits on this line with things that make both sides of this equation equal to zero. So it would be X equals four, Y equals nine, which we have right up there, and then the slope is right over here, it's negative four.
Now from this can we now express this linear equation in y-intercept form? And y-intercept form, just as a bit of a reminder, it's Y is equal to MX plus B. Where this coefficient is our slope and this constant right over here allows us to figure out our y-intercept.
And to get this in this form we just have to simplify a little bit of this algebra. So you have Y minus nine. Y minus nine is equal to, well let's distribute this negative four. And I'll just switch some colors. Let's distribute this negative four. Negative four times X is negative four X.
Negative four time negative four is plus And now, if we just want to isolate the Y on the left hand side, we can add nine to both sides. So let's do that. Let's add nine, let's add nine to both sides. Let's add nine to both sides. On the left-hand side we're just left with Y. And on the right-hand side we're left with negative four X and then 16 plus nine is plus
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