Consider the following linear equation.

y=35x+3
Step 2 of 2: Graph the line.

To graph the line represented by the equation \( y = 35x + 3 \), follow these steps:

### Step 1: Identify the Slope and Y-Intercept
- **Slope (m):** The slope of the line is 35. This means for every unit increase in \(x\), \(y\) increases by 35 units.
- **Y-Intercept (b):** The y-intercept is 3. This is the point where the line crosses the y-axis, so it has coordinates \((0, 3)\).

### Step 2: Plot the Y-Intercept
Start by plotting the y-intercept on the graph:
- Plot the point \((0, 3)\) on the y-axis.

### Step 3: Use the Slope to Find Another Point
From the y-intercept, use the slope to find another point:
- Since the slope is 35, this can be written as a rise of 35 and a run of 1. However, this is a steep slope, so a practical way to use it is:
  - From \((0, 3)\), move 1 unit to the right (increase in \(x\)) and 35 units up (increase in \(y\)). This gives you another point: \((1, 38)\).

### Step 4: Draw the Line
- Draw a straight line through the points \((0, 3)\) and \((1, 38)\).

### Step 5: Extend the Line
- Extend the line in both directions to cover the graph. Make sure to use a ruler or a straight edge to keep the line straight.

This line represents the equation \( y = 35x + 3 \).

Would you like to see an illustration of the graph, or do you have any questions?

### Related Questions
1. How do you graph a line with a negative slope?
2. What is the effect of changing the y-intercept in a linear equation?
3. How would you graph the line if the slope were a fraction, such as \( \frac{1}{2} \)?
4. What are parallel lines, and how do their equations relate?
5. How can you find the x-intercept of the line from its equation?

**Tip:** When graphing lines with steep slopes, it may be easier to use a larger scale on the graph to visualize the line more clearly.

Consider the following linear equation. y = 35x + 3. Step 2 of 2: Graph the line.

Learn how to graph the linear equation y = 35x + 3 step-by-step. This problem covers the identification of slope and y-intercept, plotting points on a graph, and drawing the line. Suitable for students in Grades 8-10.

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