Question

graph the following features: - y-intercept = 4 - slope = 3

Explanation:

Step1: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Given that the y - intercept \(b = 4\), we plot the point \((0,4)\) on the coordinate plane.

Step2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}\), and here \(m = 3=\frac{3}{1}\). This means from the point \((0,4)\), we move up 3 units (rise) and 1 unit to the right (run). So we find the next point by adding 3 to the y - coordinate and 1 to the x - coordinate of \((0,4)\). The new point is \((0 + 1,4+3)=(1,7)\).

Step3: Draw the line

Draw a straight line passing through the points \((0,4)\) and \((1,7)\) (and extending in both directions).

Answer:

The line is graphed by first plotting \((0,4)\) (the y - intercept) and then using the slope \(3\) (rise 3, run 1) to find another point \((1,7)\) and drawing a straight line through these points.