The Equation for Line CD Passing Through Points (0, 2) and (4, 6)
The equation for line CD passing through points (0, 2) and (4, 6) can be found using the slope-intercept formula.
When it comes to understanding the equation for a line passing through two given points, it’s important to grasp the fundamental principles of linear equations. In the case of line CD passing through points (0, 2) and (4, 6), we can utilize the slope-intercept form of a linear equation to determine the equation for this particular line. By analyzing the given points and identifying the slope and y-intercept, we can easily formulate the equation for line CD.
Determining the Equation for Line CD
To determine the equation for line CD passing through points (0, 2) and (4, 6), we must first calculate the slope of the line. The formula for slope is (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. By substituting the given coordinates into the formula, we find that the slope of line CD is (6 – 2) / (4 – 0) = 4 / 4 = 1. With the slope in hand, we can now move on to finding the y-intercept of the line.
Once we have the slope of 1, we can use one of the given points to solve for the y-intercept. Let’s take point (0, 2) and use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values of the slope and the coordinates of the point, we can solve for b. Substituting 1 for m, 0 for x, and 2 for y, we get 2 = 1(0) + b, which simplifies to 2 = b. Therefore, the y-intercept of line CD is 2. With the slope and y-intercept known, we can now formulate the equation for line CD passing through points (0, 2) and (4, 6).
In conclusion, by analyzing the points (0, 2) and (4, 6), we were able to determine the equation for line CD passing through these two points. The equation for line CD is y = x + 2, where the slope is 1 and the y-intercept is 2. By understanding the principles of linear equations and utilizing the slope-intercept form, we were able to accurately determine the equation for line CD. This process exemplifies the practical application of algebra in solving real-world problems involving lines and their equations.