Question

(2, 5), (4, 7), and (6, 9) - Create an equation for the line that passes through the three points above. Explain what method you used to solve this problem in words or by showing your work.

Answer 1

The equation for the line that passes through the points (2, 5), (4, 7), and (6, 9) is y = x + 3. To find the equation, we used the slope-intercept form of a linear equation and the point-slope form of a linear equation.

Step-by-step explanation:

The equation for the line that passes through the points (2, 5), (4, 7), and (6, 9) can be found using the slope-intercept form of a linear equation, which is y = mx + b. To find the equation, we need to find the slope (m) and the y-intercept (b).

To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Let's use the points (2, 5) and (4, 7) to find the slope: m = (7 - 5) / (4 - 2) = 2 / 2 = 1.

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. Using the point (2, 5) and the slope m = 1, we have: y - y1 = m(x - x1) => y - 5 = 1(x - 2).

Simplifying this equation, we get: y - 5 = x - 2. Adding 5 to both sides, we get: y = x + 3.