Equation of a Line

• 1). Calculate the difference between the x's and the y's of your two points. Do this by subtracting the x of your first point from the x of your second point. Then subtract the y of your second point from the y of your first point. For instance, if you have the points (10, 2) and (15, 12), the difference of the x's is (15-10), which is 5. The difference of the y's is (12-2), which is 10.
  
  
• 2). Calculate the slope of your line. Slope is rise over run, which is the difference of your y's over the difference of your x's. In the example, the slope of the line would be 10/5, which is 2. You now have part of the equation: y=2x+b.
  
  
• 3). Figure out the y-intercept of the line by selecting one of your points and plugging it into the equation. In the example, plugging in the first (x,y) point of (10,2) makes y=2x+b into 2=2(10)+b. Solving for b gives you 2-(2)(10)=b, or 2-20=b. Therefore, the y-intercept is -18.
  
  
• 4). Write the equation of your line with the calculated slope and y-intercept, y=mx+b. In the example, the equation is y=2x-18.
  
  

Equation of a Circle

• 1). Calculate the middle of your circle. Since you have two endpoints on the circle, the middle is halfway between those two points. For instance, if the points are (5, 6) and (8,2), then the x-coordinate of the center of the circle is (5+8)/2 and the y-coordinate is (6+2)/2. Thus, the center of the circle would be at (6.5,4).
  
  
• 2). Determine the length of the line connecting your two endpoints, which is the diameter of your circle. The length of a line is calculated by taking the square root of ((x2-x1)^2 + (y2-y1)^2). Using the points (5,6) and (8,2) in the example, take the square root of ((8-5)^2 + (2-6)^2). This simplifies to the square root of (9 + 16), which is 5.
  
  
• 3). Divide the diameter in half to get the radius of the circle, then write out the standard equation for a circle with center (h,k) and radius r: (x-h)^2 - (y-k)^2 = r^2. The equation for the example is (x-6.5)^2 - (y-4)^2 = (2.5)^2. Since (2.5)^2 is 6.25, the final equation is (x-6.5)^2 - (y-4)^2 = 6.25.