This means that we need only plot the \(x\)- and \(y\)-intercepts, then draw a line through them. Furthermore, two points completely determine a line. We know that the graph of \(2x−3y = 6\) is a line. Let’s put these rules for finding intercepts to work.įind the \(x\)- and \(y\)-intercepts of the line having equation \(2x−3y = 6\). To find the \(y\)-intercepts of the graph of an equation, substitute \(x = 0\) into the equation and solve for \(y\). Note that each of these \(y\)-intercepts has an \(x\)-coordinate equal to zero. Each of these crossing points is called a \(y\)-intercept. ![]() 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.\( \newcommand\) crosses the \(y\)-axis three times. Standard form is one of the three different ways to write linear equations. This prettier version of the equation is called. Learning How to Write Standard Form Equations An equation in standard form looks like ax by c, where b and c are integers, and a is a positive integer. 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: It is usually written as a x b y c 0 or a x b y c, where a, b and c are constants and x and y are variables. 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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