There is some overlap among these topics, so I recommend reading the whole page. Ultimately, what are the sources of errors and of misunderstanding? What kinds of biases and erroneous preconceptions do we have?
Slope-intercept form linear equations Standard form linear equations Point-slope form linear equations Video transcript A line passes through the points negative 3, 6 and 6, 0.
Find the equation of this line in point slope form, slope intercept form, standard form. And the way to think about these, these are just three different ways of writing the same equation. So if you give me one of them, we can manipulate it to get any of the other ones.
But point slope form says that, look, if I know a particular point, and if I know the slope of the line, then putting that line in point slope form would be y minus y1 is equal to m times x minus x1.
So this is a particular x, and a particular y. It could be a negative 3 and 6. Slope intercept form is y is equal to mx plus b, where once again m is the slope, b is the y-intercept-- where does the line intersect the y-axis-- what value does y take on when x is 0?
And then standard form is the form ax plus by is equal to c, where these are just two numbers, essentially. So the first thing we want to do is figure out the slope. Once we figure out the slope, then point slope form is actually very, very, very straightforward to calculate.
So, just to remind ourselves, slope, which is equal to m, which is going to be equal to the change in y over the change in x. Now what is the change in y?
If we view this as our end point, if we imagine that we are going from here to that point, what is the change in y? Well, we have our end point, which is 0, y ends up at the 0, and y was at 6. So, our finishing y point is 0, our starting y point is 6.
What was our finishing x point, or x-coordinate? Our finishing x-coordinate was 6. So this 0, we have that 0, that is that 0 right there. And then we have this 6, which was our starting y point, that is that 6 right there.
And then we want our finishing x value-- that is that 6 right there, or that 6 right there-- and we want to subtract from that our starting x value. We went from 6 to 0. Our y went down by 6. So we get 0 minus 6 is negative 6. Y went down by 6.
And, if we went from that point to that point, what happened to x? We went from negative 3 to 6, it should go up by 9. You divide the numerator and the denominator by 3. And we have our slope. We can simplify it a little bit. This is our point slope form. Now, we can literally just algebraically manipulate this guy right here to put it into our slope intercept form.
So we have slope intercept. So what can we do here to simplify this?
Negative 2 plus 6 is plus 4. Now the last thing we need to do is get it into the standard form. So the left-hand side of the equation-- I scrunched it up a little bit, maybe more than I should have-- the left-hand side of this equation is what? So this, by itself, we are in standard form, this is the standard form of the equation.
If we want it to look, make it look extra clean and have no fractions here, we could multiply both sides of this equation by 3. If we do that, what do we get?
And then 4 times 3 is Para mis visitantes del mundo de habla hispana, este sitio se encuentra disponible en español en: América Latina España. This Web site is a course in statistics appreciation; i.e., acquiring a feeling for the statistical way of thinking.
Learn why the Common Core is important for your child. What parents should know; Myths vs. facts. Recall that the slope (m) is the "steepness" of the line and b is the intercept - the point where the line crosses the y-axis. In the figure above, adjust both m and b . How To: Given two points on the curve of an exponential function, use a graphing calculator to find the equation.
Press [STAT]. Clear any existing entries in . § Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted (a) The provisions of §§ of this subchapter shall be .
Find the equation of the line that passes through the points (–2, 4) and (1, 2). Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is for. Now I have the slope and two points.