![]() You can also find b using a y-intercept calculator. Input the slope and coordinates for a known point on the line for the m, x, and y variables, respectively, in the slope-intercept form equation. If you know the slope already, then you can skip this step. If you know two points on the line, you can use the slope formula above to find it or use a slope calculator. The first step is to find the line’s slope. You can express the equation of a straight line in slope-intercept form in a few steps. Then, since point (x 2, y 2) is an arbitrary point on the line, we can rename it to just (x, y).įinally, we see that the resulting equation of the line is the slope-intercept form equation above. Now, we can substitute the y-intercept (which, by definition, is the coordinate (0, b)) for (x 1, y 1). If you multiply both sides of this equation by the denominator (x 2 – x 1), the formula can be rewritten as: The formula for slope using the coordinates for two points (x 1, y 1) and (x 2, y 2) is: Slope-intercept form is derived from the slope formula. In the slope-intercept formula, the slope of the line m is the coefficient for the x-coordinate, and the y-intercept is represented as the b variable. The slope-intercept form of a line states that the y-coordinate y of a point on the line is equal to the slope m times the x-coordinate x plus the y-intercept b. The slope-intercept form equation is given by: The y-intercept is the y-coordinate where the line crosses the y-axis. Slope-intercept form is applicable when you have the slope and y-intercept for a line or when you can calculate these for the line. The combination of these elements can be used to plot any point on the line. Slope-intercept form gets its name because the equation contains the slope and the y-intercept of the line. ![]() The slope-intercept form equation can be used to find any point on the line. Slope-intercept form is a type of linear equation format used to express a straight line. Slope-intercept form is probably the most frequently used equation format to represent a line, but you can also express the line in point-slope form or standard form. You can use a calculator like the one above to find the equation for a straight line in slope-intercept form, but you can also follow the steps below to find it. The most commonly used method is an algebraic equation in slope-intercept form. It worked out.There are several ways to describe a line using its slope, or gradient. So it is, negative 14x plus 21y is equal to 12. Of them the way I did in that previous example. If there was a common factorįor all three of these numbers then I would divide all And 21 and 12 are divisibleīy three but 14 isn't. But all of these aren'tĭivisible by the same number. 12 is divisible by two, six, three, four. Now let's see, am I done? Do these share any, do 14, 21, and 12 share any common factors? Let's see, 14 is divisibleīy two and seven. Let's see and I subtractedġ4x to get rid of this. So on the left hand side I have negative 14x plus 21y. Then what am I left with? Let me give myself a I can't just do it on the right hand side I have to do it on the So I wanna get thisġ4x onto the left side. And now I wanna get all the X's and Y's on one side. Three times seven of course isĢ1, we just figured that out. So this is going to be multiplied by three and multiplied by seven. Three and I multiply by seven, I have to do that to this side as well. So we start with Y is equal to 2/3x plus 4/7. So if you multiply threeĪnd you multiply by seven. Rid of the fractions is to multiple by threeĪnd to multiply by seven. The first thing you could try to do is well let's get rid ofĪll of these fractions. So the first thing I would wanna do is, well there's a bunch of ways Because there's obviously aīunch of forms in this way. ![]() That they're asking for and probably because it's just easier for the site to know that You get 2x, divide this by two you'll get plus y is equal to 5. Divide them all by twoĪnd then you would get two so you divide this by two. Number, and this number are all divisible by two. So if we got to the point of say 4x plus 2y is equal to 10, well this number, and this ![]() That just means that A, B,Īnd C in the standard form they want need to be integers. Which means all numbers must be integers that do not share a commonįactor other than one. And that extra text they were saying, the equation must be simplified. Which would be the form Ax plus By is equal to C. But we wanna write this in standard form. Out what the slope and what the Y intercept It's written in the form Y is equal to mx plus b, where m in this case is 2/3 and b is 4/7. So the way that it's written right now, this is slope intercept form. The equation must be simplified, which means all numbers must be integers that do not share a commonįactor other than one. Rewrite Y is equal to 2/3x plus 4/7 in standard form.
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