Question

graph the line,
$y = \frac{1}{4}x + 4$

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{1}{4}x + 4\), the y - intercept \(b = 4\). This means the line crosses the y - axis at the point \((0,4)\).

Step2: Use the slope to find another point

The slope \(m=\frac{1}{4}\), which can be thought of as \(\frac{\text{rise}}{\text{run}}=\frac{1}{4}\). Starting from the y - intercept \((0,4)\), we move up 1 unit (rise) and then 4 units to the right (run). This gives us the point \((0 + 4,4+1)=(4,5)\). We can also move down 1 unit and 4 units to the left from the y - intercept: \((0-4,4 - 1)=(-4,3)\).

Step3: Plot the points and draw the line

Plot the points \((0,4)\), \((4,5)\) (or \((-4,3)\)) on the coordinate plane. Then, use a straightedge to draw a line through these points. The line should extend in both directions.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y = \frac{1}{4}x+4\) passing through the points found above. If we were to describe the key points: the y - intercept is at \((0,4)\) and another point can be \((4,5)\) or \((-4,3)\) and the line is drawn through these points with a slope of \(\frac{1}{4}\).)

Answer:

The line \(y=\frac{1}{4}x + 4\) is graphed by plotting the y - intercept \((0,4)\) and using the slope \(\frac{1}{4}\) to find another point (e.g., \((4,5)\) or \((-4,3)\)) and then drawing a straight line through these points.