Y=3x-5

The equation you provided, \( y = 3x - 5 \), is a linear equation in slope-intercept form ( \( y = mx + b \) ), where:

• \( m \) is the slope of the line, and in this case, \( m = 3 \).
• \( b \) is the y-intercept, which means the point where the line crosses the y-axis. Here, \( b = -5 \).

Characteristics of the Line

1. Slope: The slope of 3 indicates that for every unit increase in \( x \), \( y \) increases by 3 units.
2. Y-intercept: The line crosses the y-axis at the point (0, -5).
3. X-intercept: To find the x-intercept, set \( y = 0 \): \[ 0 = 3x - 5 \implies 3x = 5 \implies x = \frac{5}{3} \] So the x-intercept is \( \left( \frac{5}{3}, 0 \right) \).

Graphing the Line

To graph the line:

1. Plot the y-intercept: Mark the point (0, -5) on the graph.
2. Use the slope to find another point: Starting from (0, -5), move up 3 units and right 1 unit to the point (1, -2). Plot this point.
3. Draw the line: Connect the two points with a straight line, extending it in both directions.

If you have any specific questions about this equation or how to manipulate or analyze it, feel free to ask!