To find the intersection point of the two given points (2,3) and (4,9), we first determine the equation of the line passing through these two points using the point-slope formula:
m = (y2 - y1) / (x2 - x1)
m = (9 - 3) / (4 - 2)
m = 6 / 2
m = 3
Using the slope-intercept form of a line equation (y = mx + b) and one of the given points (2,3), we can solve for the y-intercept (b):
3 = 3(2) + b
3 = 6 + b
b = -3
Therefore, the equation of the line passing through the points (2,3) and (4,9) is y = 3x - 3. To find the x-coordinate of the intersection point, we set the y-values equal to each other and solve for x:
3x - 3 = 9
3x = 12
x = 4
Substitute x = 4 back into the equation of the line to find the y-coordinate:
y = 3(4) - 3
y = 12 - 3
y = 9
So, the intersection point of the two given points is (4,9)