How to Graph Linear Equations by the Slope Intercept

The slope-intercept form of a linear equation is y=mx+b. m is the slope of the line that the linear equation represents. "B" is the height, or y-value, where the line intersects the x-axis. This form is not be confused with the slope form, which is m=(y-y0)/(x-x0), with (x0,y0) being any specified point on the line.

Instructions

1. Rearrange the equation to put the linear equation in the slope-intercept form. Do this by performing the same arithmetic operation on one side of the equation as you perform on the other.

   For example, 3 = (y-2)/(x-1) will need both sides multiplied by x-1 in order to bring x out of the denominator. The slope-intercept form (y=mx+b) doesn’t have any variable in denominators. Multiplying both sides by x-1 produces 3(x-1) = y-2. Rewrite it so y is on the left of the equals sign and x is on the right: y-2 = 3(x-1). Multiply out the right-hand side, since the slope-intercept method has no shared coefficients between x and any numbers: y-2 = 3x-3. Add 2 to both sides, since the slope-intercept method has no numbers on the same side of the equation with y: y = 3x-1.

2. Locate the y-intercept from the number on the right-hand side of the slope-intercept formula. The value of x is 0 when the line hits the y-axis.

   For example, for y = 3x-1, the y-intercept is -1. That’s the height where the line intersects the y-axis. So the coordinate where the line hits the y-axis is (x,y) = (0,-1). So sketch a point at (0,-1).

3. Draw from the point you sketched in Step 2 one unit to the right and m units up. If the slope, m, is negative, then draw that many units down. Mark the point where you land. Then draw a line through the two points you’ve drawn. If m is a fraction, move the denominator’s number of units to the right, and the numerator’s number of units up before drawing your point.

   For example, y = 3x-1 has slope m=3. So move one unit of x to the right from the slope-intercept you drew at (0,-1) and up three units. You’ll land at point (1,2). Now draw a line through these two points to get your line. If instead the formula was y = 3x/2 - 1, then move 2 units to the right and 3 units up, to land at (2,2). Then draw a line through (0,-1) and (2,2).

References

• Purple Math: Slope-intercept Form
• Math Warehouse: Slope-intercept Form