Question

A line passes through (4, 5) and (8, 9). Which equation best represents the line?

A. y=x+1
B. y=1
C. y=2x+1
D. y=5x+8

Answer 1

The equation that best represents the line passing through the points (4, 5) and (8, 9) is y = x + 1. This is determined by calculating the slope of the line and using one of the points to solve for the y-intercept.

Step-by-step explanation:

To determine which equation best represents the line passing through the points (4, 5) and (8, 9), we first need to calculate the slope of the line. The slope (m) is calculated by the change in y over the change in x, which is (y2 - y1) / (x2 - x1). Plugging in the given points:

m = (9 - 5) / (8 - 4) = 4 / 4 = 1

Now we have the slope, which is 1. To find the y-intercept (b), we can use one of the points and the slope in the slope-intercept form y = mx + b. Let's use the point (4, 5)
5 = (1)(4) + b

This simplifies to 5 = 4 + b, so b = 5 - 4 = 1. Therefore, the equation of the line is y = x + 1, which corresponds to option A.