Alright, let's solve the problem step by step.
### Step 1: Formulate the Equation
We start with the given equation:
[tex]\[ y = 3x + 61 - 2 \][/tex]
### Step 2: Simplify the Equation
First, simplify the equation by combining like terms:
[tex]\[ 61 - 2 = 59 \][/tex]
So, the simplified equation is:
[tex]\[ y = 3x + 59 \][/tex]
### Step 3: Generate Points
Now, we will generate a few points (x, y) from the equation. Let's choose some values for [tex]\(x\)[/tex] and compute the corresponding [tex]\(y\)[/tex] values.
For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 3(0) + 59 \][/tex]
[tex]\[ y = 59 \][/tex]
So, one point is (0, 59).
For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 3(1) + 59 \][/tex]
[tex]\[ y = 62 \][/tex]
So, another point is (1, 62).
For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 3(2) + 59 \][/tex]
[tex]\[ y = 65 \][/tex]
So, another point is (2, 65).
### Step 4: List the Points
We've generated three points:
- (0, 59)
- (1, 62)
- (2, 65)
### Step 5: Graph the Points
To graph the equation [tex]\( y = 3x + 59 \)[/tex] using these points, plot the points on the coordinate plane and draw a straight line through them.
- Plot the point (0, 59).
- Plot the point (1, 62).
- Plot the point (2, 65).
Connecting these points with a straight line will give you the graph of the equation [tex]\( y = 3x + 59 \)[/tex].
By following these steps, you have successfully graphed the equation using the provided points.
