With the circle's center point also an ( x, y ) value, you can create a right triangle with the two sides x boxes left or right from that center point, and y boxes up or down from that same center point. Move right or left so many boxes (that's the x value), and then move up or down to the y value. When you consider a circle on a coordinate graph is the set of all points equidistant from a center point, you can see that those points can be described as an ( x, y ) value on the graph. The second formula applies either the standard form or general form for the equation. The first takes advantage of the Pythagorean Theorem. Finding common factors to convert equations with fractions into standard form equations makes it easier to move onto more complex math concepts, like graphing linear equations.Circles are everywhere, and every circle can be described mathematically by either of two formulas. Standard form is one of the three different ways to write linear equations.
STANDARD FORM EQUATION HOW TO
Learning How to Write Standard Form Equations
We can do this by multiplying both sides of the equation by -1: Now that all the coefficients in this equation are whole numbers, we need to convert -6 into a positive number. The least common denominator of these two numbers is 8, so let's multiple each side by this: To do this, we must determine the common factors of the two denominators, -4 and 8. The first step is removing the fractions from the equations. Let's convert the below equation, which contains fractions and negative numbers, into a proper standard form equation: Once you rearrange this equation to be in the y = mx + b format, this equation is in slope-intercept form:Īs we've stated, in standard form, equations coefficients A, B, and C must be whole numbers. Now, we must divide both sides by -2 to isolate the y: We want to isolate the y, so let’s start by subtracting 6x from both sides:Īs you can see, you’re left with -2y on the left. Let’s convert the following standard form equation to slope-intercept form: Converting Standard Form to Slope-Intercept Form Since this is a useful form, you’ll often be asked to convert an equation from standard form to slope-intercept form. The slope-intercept form has the slope, m, and the y-intercept, b, on the right-hand side of the equation. In point-slope form, x1 and y1 are coordinates of a point on a graphed line, and m is the line's slope. All you have to do is plug in a 0 for the y to find the x-intercept or a 0 for the x to find the y-intercept. Writing an equation in standard form makes it easier to find the x and y-intercepts, which is where the graph crosses the x- and y-axis. Linear equations come in different forms, like point-slope form and slope-intercept form.
Point-Slope, Slope-Intercept, and Standard Form EquationsĪ linear equation is the equation of a line on a graph. In the standard form equation, coefficients B and C can be positive or negative numbers, but coefficient A must be a positive number. The standard form equation is a linear equation that contains two variables, usually (but not limited) to x-terms and y-terms, that are on the same sides of the equation: Ax + By = CĬoefficients A, B, and C must be whole number integers that have no decimals or fractions.
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