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To graph the line with slope \(-3\) passing through the point \((1, 1)\), we need to follow these steps:

1. **Point-Slope Form**: The equation of a line in point-slope form is:

   \[
   y - y_1 = m(x - x_1)
   \]

   where \(m\) is the slope and \((x_1, y_1)\) is a point on the line. In this case, the point is \((1, 1)\) and the slope \(m = -3\). Substituting into the formula:

   \[
   y - 1 = -3(x - 1)
   \]

2. **Simplifying**:

   \[
   y - 1 = -3x + 3
   \]
   \[
   y = -3x + 4
   \]

   This is the equation of the line in slope-intercept form, \(y = -3x + 4\), which tells us the slope is \(-3\) and the y-intercept is \(4\).

3. **Plotting the Graph**:
   - Start by plotting the point \((1, 1)\) on the graph.
   - From this point, use the slope \(-3\), which means for every \(1\) unit you move to the right (increase in \(x\)), you move \(3\) units down (decrease in \(y\)).

4. **Finding another point**:
   - From \((1, 1)\), move right \(1\) unit to \(x = 2\), then move down \(3\) units to \(y = -2\). So, another point on the line is \((2, -2)\).

5. **Drawing the Line**:
   - Now, draw a straight line passing through the points \((1, 1)\) and \((2, -2)\).

Would you like further details or clarification on how to graph the line?

Here are 5 related questions:
1. How do you determine the slope of a line from its graph?
2. What is the general form of a linear equation, and how does it relate to slope-intercept form?
3. How would the graph change if the slope was positive instead of negative?
4. How do you find the x-intercept of a line given its equation?
5. What is the difference between point-slope form and slope-intercept form of a line?

**Tip**: When graphing lines, always remember that the slope tells you how much the line rises or falls as you move horizontally across the graph.

Graph the line with slope -3 passing through the point (1,1).

Learn how to graph a line with a slope of -3 passing through the point (1,1). This solution includes the point-slope form equation, how to simplify to slope-intercept form, and the process of plotting the line. Suitable for students in Grades 8-10.

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