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The slope-intercept form is one of the easiest ways to represent a linear equation. The formula is given by:

\( y = mx + b \). Here, \( m \) represents the slope, which indicates how steep the line is, and \( b \) is the y-intercept, which is where the line crosses the y-axis.

Knowing this form makes it simple to write the equation of a line once you have the slope and y-intercept. For example, in the problem, we get the slope \( m = \frac{4}{3} \) and find the y-intercept \( b = -2.67 \). So, the full equation is \( y = \frac{4}{3}x - 2.67 \).

To sum it up:

• \( y = mx + b \) is the slope-intercept form.
• \( m \) is the slope.
• \( b \) is the y-intercept.

Finding the y-intercept can feel like solving a puzzle. But once you break it down, it's quite simple.

To find the y-intercept \( b \), use the point given in the problem, \( (-1, -4) \), and substitute it into the slope-intercept form along with the slope \( m \). Here's how it works:

1. Start with the basic equation: \( y = mx + b \).
2. Substitute \( x = -1 \) and \( y = -4 \) to get: \( -4 = \frac{4}{3}(-1) + b \).
3. Simplify: \( -4 = -\frac{4}{3} + b \).
4. Add \( \frac{4}{3} \) to both sides to isolate \( b \): \( b = -4 + \frac{4}{3} \).

By solving this, you'll find that \( b = -2.67 \). Now you have the y-intercept, which is essential for graphing the line.

Graphing a line is a visual way to understand its equation. Here is a straightforward method to graph using the slope-intercept form.

1. Start by plotting the y-intercept \( (0, -2.67) \). This is where your line crosses the y-axis.

2. Use the slope to find another point. Slope \( m = \frac{4}{3} \) means that for every 3 units you move to the right on the x-axis, you move 4 units up on the y-axis.
3. From \( (0, -2.67) \), count 3 units to the right (x direction) and 4 units up (y direction) to locate a new point.

• This new point will help you draw your line accurately.
• In our case, if we start from (0, -2.67), by moving to (3, 1.33), we get another point.

4. Connect these points with a straight line. This line represents your equation \( y = \frac{4}{3}x - 2.67 \).

Following these steps will help you graph any line given its slope and y-intercept.