Linear equations graph as a straight line using the slope intercept form of y = mx + b, where "m" is the slope and "b" is the y-intercept, or point where the line crosses the y-axis. The y-intercept can be used to find additional points for the line. The slope, which represents movement on the y-axis followed by movement on the x-axis, can be added to the y-intercept to find another point. For example, a slope of 5 and a y-intercept of 3, or point (0,3), would create an additional point of (0 + 1, 3 + 5) = (1,8).
Graph a linear equation by converting it to slope intercept form, determining the slope and y-intercept and then graphing points, beginning with the intercept. Use the linear equation 6y = 6x + 5 as an example. Divide both sides by 6: y = x + (5/6), where the slope is 1 and the y-intercept is (5/6) or point (0,5/6).
Convert a fractional y-intercept to decimal form to make it easier to graph. Divide the numerator by the denominator: 5 / 6 = 0.833... or 0.83 (rounded). Draw the y-intercept point on the graph by visually estimating a point on the y-axis that is slightly below the 1.
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Find additional points for the line using the slope and y-intercept in decimal form by adding the slope two times and subtracting the slope two times, to give a better view of what the line looks like. Note that the slope is 1 or 1/1: (0 + 1, 0.83 + 1) = (1,1.83) and (1 + 1, 1.83 + 1) = (2,2.83); (0 - 1, 0.83 - 1) = (-1,-0.17) and (-1 - 1, -0.17 - 1) = (-2,-1.17).
Graph the points and draw a straight line, placing arrows on each end to represent continuation.