Final answer:
To find the equation of the line, we calculate the slope using the two points, which is 2, and then apply it to the point-slope form. The equation of the line that passes through (1,5) and (3,9) is y = 2x + 3.
Step-by-step explanation:
To find the equation of the line passing through the points (1,5) and (3,9), we first need to determine the slope (m) of the line.
The slope can be found by using the slope formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. Plugging in our points, we get:
m = (9 - 5) / (3 - 1)
= 4 / 2
= 2
Now that we have the slope, we can use the point-slope form of the line equation, y - y1 = m(x - x1), with either of the given points. Let's use the point (1,5):
y - 5 = 2(x - 1)
Simplifying this equation, we get:
y = 2x + 3
This is the equation of the line passing through the points (1,5) and (3,9).