- 1). Put the two equations into slope-intercept form (y=mx+b). In the slope-intercept form, "m" represents slope, while "b" gives the y-intercept. Start with the following two example equations: f(x) = 2x + 3 and
g(x) = -0.5x + 7 - 2). Set your equations equal to each other. Remember that anytime you move something to the other side of the equals sign, the value changes from positive to negative (and vice-versa). One equation should be on one side of the equals sign and the other equation on the other side. Your two equations should now look like this: 2x+3=-0.5x+7
- 3). Solve your equation for x by isolating x to either the right side or left side of the equals sign. As mentioned in Step 2, if you move a number from one side of the equals sign to the other, the sign should change, from negative to positive and vice-versa. The steps for solving for "x" are as follows: 2.5x=4, then x=4/2.5 and, finally x=1.6.
- 4). Plug the value for x into your original two equations and obtain a y value. The x and y values you obtain will be the (x,y) for your point of intersection. This y calculation looks like this:
y = -0.5x + 7
y = -0.5(1.6) + 7
y = -0.8 + 7
y = 6.2
y = 2x + 3
y =2(1.6) + 3
y = 3.2 + 3
y = 6.2 - 5). Plot your point of intersection on graph paper and extend the two rays to see if the rays truly intersect. Make certain that if you can't draw straight lines freehand to use a ruler in order to accurately trace straight lines on paper.
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