Final answer:
To find the equation of the line passing through the points (2, 5) and (4, 9), we can use the slope-intercept form of a linear equation, which is y = mx + b. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), and the y-intercept (b) can be found by substituting the coordinates of one of the points and the slope into the equation: y = mx + b. Therefore, the equation of the line passing through the given points is y = 2x + 1. Option number a is correct.
Step-by-step explanation:
To find the equation of the line passing through the points (2, 5) and (4, 9), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
Plugging in the values from the given points, we get m = (9 - 5) / (4 - 2) = 4/2 = 2.
Next, let's find the y-intercept (b) by substituting the coordinates of one of the points and the slope into the equation: y = mx + b. Using the point (2, 5) and the slope m = 2, we substitute these values to get 5 = 2(2) + b. Solving for b, we get b = 5 - 4 = 1.
Therefore, the equation of the line passing through the points (2, 5) and (4, 9) is y = 2x + 1, which corresponds to option A.