Question

5 graph the equation: $y = \frac{1}{4}x + 1$

Explanation:

Step1: Identify the slope and y - intercept

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

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,1)\) (since when \(x = 0\), \(y=1\)) and mark it.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{4}\) can be thought of as \(\frac{\text{rise}}{\text{run}}\). So, from the point \((0,1)\), we move up 1 unit (rise) and then move 4 units to the right (run). This will give us the point \((0 + 4,1+1)=(4,2)\). We can also move down 1 unit and left 4 units from \((0,1)\) to get the point \((0-4,1 - 1)=(-4,0)\) (this is helpful for drawing a more accurate line).

Step4: Draw the line

Connect the points (for example, \((0,1)\), \((4,2)\) and \((-4,0)\)) with a straight line. This line represents the graph of the equation \(y=\frac{1}{4}x + 1\).

(Note: Since the question is about graphing, the final answer is the graph of the line passing through \((0,1)\), \((4,2)\), \((-4,0)\) etc. following the steps above. If we were to describe the key points, the line has a y - intercept at \((0,1)\) and passes through \((4,2)\) as well.)

Answer:

The graph of \(y = \frac{1}{4}x+1\) is a straight line with a y - intercept at \((0,1)\) and passing through points like \((4,2)\) (or \((-4,0)\)) when drawn on the given coordinate plane.