How to Write Linear Equations in Algebra By Mary Freeman; Updated April 24, Algebraic linear equations are mathematical functions that, when graphed on a Cartesian coordinate plane, produce x and y values in the pattern of a straight line. The standard form of the linear equation can be derived from the graph or from given values.
Equations in general linear form look like this: General linear form is not the most useful form to use when writing an equation from a graph. However, the form highlights certain abstract properties of linear equations, and you may be asked to put other linear equations into this form.
To write an equation in general linear form, given a graph of the equation, first find the x-intercept and the y-intercept -- these will be of the form a, 0 and 0, b.
Finally, one should try to multiply or divide both sides of the equation by a number to make the coefficients as simple as possible. For instance, if a and b are fractions, one can multiply both sides by a common denominator to obtain integer coefficients.
Once the coefficients are integers, one can divide by their greatest common divisor to simplify even further. If a or b is negative, take the positive least common multiple; i. A or B will be negative, since we will be dividing a positive number by a negative number.
Write an equation of the following line in general linear form: Graph of a Line The x-intercept is 4, 0 and the y-intercept is 0, 3. The LCM of 4 and 3 is Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information.
All you need to know is the slope (rate) and the y-intercept. Writing linear equations in Slope-Intercept Form: To write an equation of the line in slope intercept form you have a framework that requires only the slope and the y coordinate of the y-intercept. 4 Writing Linear Functions Writing Equations in Slope-Intercept Form Writing Equations in Point-Slope Form Writing Equations in Standard Form Writing Equations of Parallel and Perpendicular Lines Scatter Plots and Lines of Fit Analyzing Lines of Fit Arithmetic Sequences Online Auction (p.
) Old Faithful Geyser (p. ) School Spirit (p. ). All the pairs of numbers that are solutions of a linear equation in two variables form a line in the Euclidean plane, and every line may be defined as the solutions of a linear equation.
This is the origin of the term linear for qualifying this type of equations. Write the standard form of the equation of the line through the given point with the given slope. 9) through: Writing Linear Equations Date_____ Period____ Write the slope-intercept form of the equation of each line.
1) 3 x − 2y = −16 y = 3 2 x + 8 2) 13 x − 11 y = −12 y = 13 11 x + 12 Write the standard form of the equation of the line through the given point with the given slope. 9) through: Writing Linear Equations Date_____ Period____ Write the slope-intercept form of the equation of each line.
1) 3 x − 2y = −16 y = 3 2 x + 8 2) 13 x − 11 y = −12 y = 13 11 x + 12