-3x+1y is less than or equal to -3 graph it

To graph the inequality \(-3x + y \leq -3\), we need to follow these steps:

### Step 1: Rewrite the inequality in slope-intercept form
The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. First, solve for \(y\):

\[
-3x + y \leq -3
\]

Add \(3x\) to both sides:

\[
y \leq 3x - 3
\]

### Step 2: Graph the boundary line
The boundary line corresponds to the equation \(y = 3x - 3\). Since the inequality is "less than or equal to," the line will be **solid**, indicating that points on the line are included in the solution.

1. **Slope:** \(3\) (rise/run = 3/1)
2. **Y-intercept:** \(-3\) (this is where the line crosses the y-axis)

Plot the y-intercept at \((0, -3)\), then use the slope to find another point. From \((0, -3)\), move up 3 units and 1 unit to the right to get the point \((1, 0)\).

### Step 3: Shade the region
Since the inequality is \(y \leq 3x - 3\), you will shade **below** the line, because \(y\) is less than or equal to the line.

I'll graph this for you:

1. A solid line through \((0, -3)\) and \((1, 0)\).
2. Shaded region below the line.

Let me know if you'd like me to generate a visual representation of the graph!

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Would you like more details on this process? Here are some questions to deepen your understanding:

1. How do you convert inequalities to slope-intercept form?
2. What does the slope of a line represent in a graph?
3. Why do we use a solid line for \( \leq \) or \( \geq \) inequalities?
4. How do you determine which region to shade in an inequality graph?
5. What would change if the inequality were \( y > 3x - 3 \)?

**Tip:** Always check if you need to flip the inequality when multiplying or dividing by negative numbers!

3x + y is less than or equal to -3 graph it

Learn how to graph the linear inequality 3x + y ≤ -3. This problem covers key algebraic concepts, including rewriting in slope-intercept form, identifying the slope and y-intercept, and shading the appropriate region. Perfect for students in Grades 7-10.

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