Final answer:
To find the equation of the line through points (2,3) and (5,9), calculate the slope, which is 2, and then use one point to find the y-intercept, which is -1. Therefore, the equation of the line is y = 2x - 1.
Step-by-step explanation:
To find the equation of the line that passes through the points (2,3) and (5,9), we first need to calculate the slope of the line.
The slope (m) is the rise over the run, which can be calculated by the difference in the y-coordinates divided by the difference in the x-coordinates.
Slope (m) = (y2 - y1) / (x2 - x1)
= (9 - 3) / (5 - 2)
= 6 / 3 = 2.
Now that we know the slope, we can use one of the points to find the y-intercept (b) of the equation using the slope-intercept form, which is y = mx + b.
Let's use point (2,3).
3 = 2(2) + b
=> b
= 3 - 4
=> b
= -1.
Thus, the equation of the line is y = 2x - 1.