Answer :
Let's begin by understanding and solving the given equation:
[tex]\[ -9 = -3x \][/tex]
### Step-by-Step Solution
1. Isolate the Variable:
The goal is to solve for [tex]\( x \)[/tex]. To do that, we need to isolate [tex]\( x \)[/tex] on one side of the equation. We can do this by dividing both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[ \frac{-9}{-3} = \frac{-3x}{-3} \][/tex]
2. Simplify:
Simplifying both sides of the equation, we get:
[tex]\[ 3 = x \][/tex]
So, the solution to the equation [tex]\( -9 = -3x \)[/tex] is:
[tex]\[ x = 3 \][/tex]
### Drawing a Graph
1. Rewrite the Equation:
We can rewrite the equation [tex]\( -9 = -3x \)[/tex] in the slope-intercept form of a linear equation (i.e., [tex]\( y = mx + b \)[/tex]):
[tex]\[ y = -3x + (-9) \][/tex]
Here, [tex]\( y \)[/tex] represents the left side of the initial equation, and [tex]\( x \)[/tex] represents the variable we are solving for.
2. Plot the Equation:
To graph this equation, we need at least two points. Let's find the [tex]\( y \)[/tex]-value for two different [tex]\( x \)[/tex]-values:
- When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -3(0) + (-9) = -9 \][/tex]
So, one point is [tex]\((0, -9)\)[/tex].
- When [tex]\( x = 1 \)[/tex]:
[tex]\[ y = -3(1) + (-9) = -3 - 9 = -12 \][/tex]
So, another point is [tex]\((1, -12)\)[/tex].
3. Draw the Line:
Plot the points [tex]\((0, -9)\)[/tex] and [tex]\((1, -12)\)[/tex] on a coordinate plane and draw a straight line through them.
4. Find the Intersection:
The graph of [tex]\( y = -3x - 9 \)[/tex] is a straight line. To solve the original equation graphically, observe where this line intersects the x-axis (i.e., where [tex]\( y = 0 \)[/tex]).
Set [tex]\( y = 0 \)[/tex]:
[tex]\[ 0 = -3x - 9 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = -9 \][/tex]
[tex]\[ x = 3 \][/tex]
Thus, the graphical solution confirms our algebraic result:
[tex]\[ x = 3 \][/tex]
### Conclusion
The solution to the equation [tex]\( -9 = -3x \)[/tex] is [tex]\( x = 3 \)[/tex]. The graph of this linear equation intersects the x-axis at [tex]\( x = 3 \)[/tex], which matches our calculated solution.
[tex]\[ -9 = -3x \][/tex]
### Step-by-Step Solution
1. Isolate the Variable:
The goal is to solve for [tex]\( x \)[/tex]. To do that, we need to isolate [tex]\( x \)[/tex] on one side of the equation. We can do this by dividing both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[ \frac{-9}{-3} = \frac{-3x}{-3} \][/tex]
2. Simplify:
Simplifying both sides of the equation, we get:
[tex]\[ 3 = x \][/tex]
So, the solution to the equation [tex]\( -9 = -3x \)[/tex] is:
[tex]\[ x = 3 \][/tex]
### Drawing a Graph
1. Rewrite the Equation:
We can rewrite the equation [tex]\( -9 = -3x \)[/tex] in the slope-intercept form of a linear equation (i.e., [tex]\( y = mx + b \)[/tex]):
[tex]\[ y = -3x + (-9) \][/tex]
Here, [tex]\( y \)[/tex] represents the left side of the initial equation, and [tex]\( x \)[/tex] represents the variable we are solving for.
2. Plot the Equation:
To graph this equation, we need at least two points. Let's find the [tex]\( y \)[/tex]-value for two different [tex]\( x \)[/tex]-values:
- When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -3(0) + (-9) = -9 \][/tex]
So, one point is [tex]\((0, -9)\)[/tex].
- When [tex]\( x = 1 \)[/tex]:
[tex]\[ y = -3(1) + (-9) = -3 - 9 = -12 \][/tex]
So, another point is [tex]\((1, -12)\)[/tex].
3. Draw the Line:
Plot the points [tex]\((0, -9)\)[/tex] and [tex]\((1, -12)\)[/tex] on a coordinate plane and draw a straight line through them.
4. Find the Intersection:
The graph of [tex]\( y = -3x - 9 \)[/tex] is a straight line. To solve the original equation graphically, observe where this line intersects the x-axis (i.e., where [tex]\( y = 0 \)[/tex]).
Set [tex]\( y = 0 \)[/tex]:
[tex]\[ 0 = -3x - 9 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = -9 \][/tex]
[tex]\[ x = 3 \][/tex]
Thus, the graphical solution confirms our algebraic result:
[tex]\[ x = 3 \][/tex]
### Conclusion
The solution to the equation [tex]\( -9 = -3x \)[/tex] is [tex]\( x = 3 \)[/tex]. The graph of this linear equation intersects the x-axis at [tex]\( x = 3 \)[/tex], which matches our calculated solution.
