Answer:
[tex]2.\ \ (4,6)[/tex]
[tex]4.\ \ (0,0)[/tex]
[tex]5.\ \ (2\frac{1}{2},3\frac{3}{4})[/tex]
Step-by-step explanation:
Given
[tex]y = 1\frac{1}{2}x[/tex]
Required
Determine if the given points is on the graph
First,, we rewrite [tex]y = 1\frac{1}{2}x[/tex] as
[tex]y = \frac{3}{2}x[/tex]
[tex]1.\ \ (1\frac{1}{2},1)[/tex]
This can be interpreted as:
[tex]x = 1\frac{1}{2}[/tex]
[tex]y = 1[/tex]
Substitute [tex]x = 1\frac{1}{2}[/tex]
[tex]y = \frac{3}{2} * 1\frac{1}{2}[/tex]
[tex]y = \frac{3}{2} * \frac{3}{2}[/tex]
[tex]y = \frac{9}{4}[/tex]
This isn't equal to the given value of y.
Hence: [tex](1\frac{1}{2},1)[/tex] is not a point on the graph
[tex]2.\ \ (4,6)[/tex]
Here,
[tex]x = 4[/tex]
[tex]y = 6[/tex]
Substitute [tex]x = 4[/tex]
[tex]y = \frac{3}{2} * 4[/tex]
[tex]y = \frac{3 * 4}{2}[/tex]
[tex]y = \frac{12}{2}[/tex]
[tex]y = 6[/tex]
This point is on the graph
[tex]3.\ \ (18,12)[/tex]
Here,
[tex]x = 18[/tex]
[tex]y = 12[/tex]
Substitute [tex]x = 18[/tex]
[tex]y = \frac{3}{2} * 18[/tex]
[tex]y = \frac{3 * 18}{2}[/tex]
[tex]y = \frac{54}{2}[/tex]
[tex]y = 27[/tex]
This isn't equal to the given value of y.
Hence: [tex](18,12)[/tex] is not a point on the graph
[tex]4.\ \ (0,0)[/tex]
Here, we have
[tex]x = 0[/tex]
[tex]y = 0[/tex]
Substitute [tex]x = 0[/tex]
[tex]y = \frac{3}{2} * 0[/tex]
[tex]y = 0[/tex]
Hence:
This point is on the graph
[tex]5.\ \ (2\frac{1}{2},3\frac{3}{4})[/tex]
Here
[tex]x =2\frac{1}{2}[/tex]
[tex]y = 3\frac{3}{4}[/tex]
Substitute [tex]x =2\frac{1}{2}[/tex]
[tex]y = \frac{3}{2} * 2\frac{1}{2}[/tex]
[tex]y = \frac{3}{2} * \frac{5}{2}[/tex]
[tex]y = \frac{15}{4}[/tex]
[tex]y = 3\frac{3}{4}[/tex]
Hence:
This point is on the graph
