How to Transform a Table to Linear Equations
- 1). Calculate the slope of the linear equation by subtracting the y values of two points, subtracting the x values of two points and then dividing the former by the latter. If you were to choose the row with the point (3, 4) and the row with the point (9, 12), you would add 4 and 12 to get 16, add 3 and 9 to get 12 and then divide 16 by 12 to get a slope of 4/3.
- 2). Plug the slope and one point into the standard form of a linear equation, which is y = mx + b. Given a slope of 4/3 and the point (3, 4), the equation would read: 4 = 4/3(3) + b.
- 3). Solve for the y-intercept by solving for b. Given the equation 4 = 4/3(3) + b, you would multiply 4/3 by 3 to get 4 and then subtract 4 from both sides to get a y-intercept of 0.
- 4). Insert the y-intercept and slope into the standard form of a linear equation. Given a slope of 4/3 and a y-intercept of 0, the equation would be y = 4/3x + 0, or y = 4/3x.
- 5). Confirm the equation is correct by plugging in another point from the table. Given another point (27, 36), the equation would read 36 = 4/3 * 27. 4/3 * 27 is 36, so the equation is correct.
