Question

Determine whether each point lies on the graph of the equation.(a) 2x - y - 3 = 0 (a) (1, 2)Yes, the point is on the graph.No, the point is not on the graph.(b) (1, -1)Yes, the point is on the graph.No, the point is not on the graph.

Answer 1

a) (1, 2) not on the graph.

b) (1, -1) is on the graph.

Explanation:

Given the equation of the line as:

`2x - y - 3 = 0`

The points given are

a) (1, 2)

To determine whether it is on the graph of the line or not.

To do so, we can do 2 things:

1. Draw the graph and plot the point on the graph to check whether it is on the graph or not.

2. To put the point in the given equation of the line, whether the equation is satisfied or not.

For method 1: Kindly refer to the attached image of the line and point plotted.

Method 2:

Let us put
`x=1, y=2` in the Left Hand Side (LHS) of equation.

`2* 1 - 2 - 3\\\Rightarrow -3 \\eq 0 , RHS`

(1, 2) Not on the graph.

(b) (1, -1)

For method 1: Kindly refer to the attached image of the line and point plotted.

Method 2:

Let us put
`x=1, y=-1` in the Left Hand Side (LHS) of equation.

`2* 1 - (-1) - 3\\\Rightarrow 3-3 = 0 = RHS`

(1, -1) is on the graph.