Find four solutions for each question and graph the equation.
y=2x-3
The answer to this question is any point (x,y) which lies on the lien.
To find points that lie on the line, substitute any finite value of x, and evaluate y. Present the answer as a coordinate pair (x,y).
For example,
let x=1, y=2x-3=2(1)-3=-1
So (1,-1) is a point on the line (a solution to the linear equation).
y=2x-3
When x=0
y=2(0)-3
y=0-3
y= -3
When x=1
y=2(1)-3
y=2-3
y= -1
When x=2
y=2(2)-3
y=4-3
y= 3
When x=3
y=2(3)-3
y= 6-3
y=3
The four solutions are:-
(0,3) (1,-1) (2,3) (3,3)
As the solutions have been found draw a graph and plot them.
To find solutions for the equation y = 2x - 3, we can choose values for x and then calculate the corresponding y values.
Let's choose four different values for x and calculate their corresponding y values:
Solution 1:
When x = 0,
y = 2(0) - 3
y = 0 - 3
y = -3
So, one solution is (0, -3).
Solution 2:
When x = 1,
y = 2(1) - 3
y = 2 - 3
y = -1
So, the second solution is (1, -1).
Solution 3:
When x = -2,
y = 2(-2) - 3
y = -4 - 3
y = -7
So, the third solution is (-2, -7).
Solution 4:
When x = 3,
y = 2(3) - 3
y = 6 - 3
y = 3
Therefore, the fourth solution is (3, 3).
Now, let's graph the equation y = 2x - 3:
To plot these solutions on a graph, we create a coordinate plane with x and y-axis.
The points for the solutions we found are:
(0, -3), (1, -1), (-2, -7), (3, 3).
We plot these points on the graph and connect them with a straight line.