How to Graph & Write Linear Equations
Linear equations are especially useful to describe the relationship between two or more variables. In a linear equation, each variable is modified only by a coefficient (a number by which it is multiplied). Variables are directly related if an increase in one corresponds to an increase in another. Conversely, variables are inversely related if an increase in one corresponds to a decrease in another. Linear equations will always graph onto the coordinate plane as straight lines.
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Instructions
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Slope-Intercept Equation
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1
Isolate the variable y in your equation. For example, if an equation is written 3y + 6x = 12 (this notation is called Standard Form), solve for y:
3y = -6x + 12
y = -2x + 4 -
2
Locate the slope of the line. The slope is the number by which x is multiplied, also called a coefficient. In y = -2x + 4, the slope is -2.
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3
Locate the y-intercept. This is the constant number in the equation that is not multiplied by a variable. In y = -2x + 4, the y-intercept is 4.
Graphing
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4
Plot the y-intercept point on a coordinate plane. The y-intercept is the b value in y = mx + b. This corresponds to a point along the y-axis.
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5
Locate the slope of your line. The slope is the m value in y = mx + b. This corresponds to the vertical change of your line for every unit of left-to-right horizontal change. For example, a slope of 5 corresponds to a 5-unit vertical increase for each 1-unit moved horizontally. A negative slope corresponds to a vertical decrease.
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6
Draw a line of appropriate slope that goes through the y-intercept. If you need other points of reference, you can use the slope-intercept equation to calculate coordinates. Input a desired x-value, and the equation will compute the corresponding y-value. These paired values constitute a point on the line, which you can mark on the graph.
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