What is the slope-intercept form of a line given a slope of 3 and a y-intercept of -4?

The **slope-intercept form** of a linear equation is given by: \[ y = mx + b \] where: - \( m \) is the **slope** of the line. - \( b \) is the **y-intercept**, which is the point where the line crosses the y-axis. Given: - **Slope (\( m \))** = 3 - **Y-intercept (\( b \))** = -4 Plugging these values into the slope-intercept formula: \[ y = 3x - 4 \] **So, the slope-intercept form of the line is:** \[ y = 3x - 4 \] **Graphical Interpretation:** - **Slope (3):** For every 1 unit increase in \( x \), \( y \) increases by 3 units. - **Y-intercept (-4):** The line crosses the y-axis at the point (0, -4). **Example Points on the Line:** 1. When \( x = 0 \): \[ y = 3(0) - 4 = -4 \] Point: (0, -4) 2. When \( x = 1 \): \[ y = 3(1) - 4 = -1 \] Point: (1, -1) 3. When \( x = 2 \): \[ y = 3(2) - 4 = 2 \] Point: (2, 2) You can plot these points on a graph and draw a straight line through them to visualize the equation \( y = 3x - 4 \).