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The slope-intercept form is a way of writing the equation of a straight line. It helps us quickly identify the slope and the y-intercept of the line. The slope-intercept form of a linear equation is written as: \( y = mx + b \). Here, \( m \) represents the slope, which tells us how steeply the line rises or falls. The \( b \) is the y-intercept, which is the point where the line crosses the y-axis. When using this form, you can easily graph the line on a coordinate plane by starting at the y-intercept \( (0, b) \). Then, use the slope \( m \) to find other points on the line by rising and running accordingly.

Finding the y-intercept is a key step in writing the equation of a line in slope-intercept form. To find the y-intercept \( b \), we use a known point on the line. Let's illustrate this with our given point \( (3,0) \).1. Start by plugging the x and y values from the point into the slope-intercept equation. Since our slope \( m \) is 2, we write it as:

• \( y = 2x + b \)
• Substituting \( x = 3 \) and \( y = 0 \), we get:
• \( 0 = 2(3) + b \)
• \( 0 = 6 + b \)

Simplify the equation to solve for \( b \):

• \( b = -6 \)

So, the y-intercept is -6. This means the line crosses the y-axis at the point (0, -6).

Graphing linear functions involves plotting points and drawing a line through them. Let's graph the line we found earlier with the equation \( y = 2x - 6 \).1. **Start by plotting the y-intercept**: Since the y-intercept \( b \) is -6, we mark the point (0, -6) on the y-axis.2. **Use the slope to find another point**: Our slope \( m \) is 2, which means for every 1 unit we move to the right (positive direction on the x-axis), we move 2 units up (positive direction on the y-axis). Starting at (0, -6), move 1 unit to the right to (1, -6) and then 2 units up to (1, -4).3. **Draw the line**: With the points (0, -6) and (1, -4), draw a straight line through them. This line represents the graph of the equation \( y = 2x - 6 \).Using these steps, you can graph any linear function by identifying the y-intercept and using the slope to determine additional points.