A line with a slope of 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. The slope of the line is 3/2, which means for every increase of 3 units in the y-direction, there is an increase of 2 units in the x-direction. Starting from the point (1,3), we can apply this slope to find another point on the line. By moving up 3 units from y=3, we get y=6, and by moving right 2 units from x=1, we get x=3. Therefore, (3,6) is on the line.
b. To determine if the point (0,0) is on the line, we can substitute x=0 and y=0 into the equation of the line. Plugging x=0 into the equation y = (3/2)x + b, we get y = (3/2)*0 + b = b. Therefore, b = 3. So, the equation of the line is y = (3/2)x + 3. This equation does not hold true for the point (0,0), so (0,0) is not on this line.
c. To determine if the point (13,22) is on the line, we can substitute x=13 and y=22 into the equation of the line. Plugging x=13 into the equation y = (3/2)x + b, we get y = (3/2)*13 + b = 19.5 + b. However, y=22, so 22 does not equal 19.5 + b. Therefore, (13,22) is not on this line.
make all your answer a sentence
a. The point (3,6) is on this line because by applying the slope of 3/2 to the initial point (1,3), we find that moving up by 3 units and right by 2 units satisfies the equation for the line.
b. The point (0,0) is not on this line as substituting x=0 into the equation y = (3/2)x + 3 does not result in y=0.
c. The point (13,22) is not on this line as substituting x=13 and y=22 into the equation y = (3/2)x + b does not result in an equation that holds true.