A line with slope 3/2 passes through the point (1,3).
a. Explain why (3,6) is on this line
b. Explain why (0,0) is not on this line.
c. Is the point (13,22) on this line? Explain why or why not.
a. To show that the point (3,6) is on the line with slope 3/2 passing through (1,3), we can calculate the slope between these two points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (6 - 3) / (3 - 1)
Slope = 3 / 2
Since the slope between (3,6) and (1,3) is the same as the slope of the line, the point (3,6) lies on the line.
b. To show that the point (0,0) is not on the line with slope 3/2 passing through (1,3), we can calculate the slope between these two points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (0 - 3) / (0 - 1)
Slope = -3 / -1
Slope = 3
Since the slope between (0,0) and (1,3) is not equal to the slope of the line, the point (0,0) does not lie on the line.
c. To determine if the point (13,22) is on the line, we can substitute the coordinates into the equation of the line and check if it satisfies the equation y = (3/2)x + b:
Since the line passes through the point (1,3):
3 = (3/2)(1) + b
3 = 3/2 + b
b = 3 - 3/2
b = 3/2
So, the equation of the line is y = (3/2)x + 3/2. Substituting the point (13,22) into the equation:
22 = (3/2)(13) + 3/2
22 = 39/2 + 3/2
22 = 42/2
22 = 22
Since the equation is satisfied, the point (13,22) lies on the line with slope 3/2 passing through (1,3).