Question

1. $y = \frac{1}{4}x + 2$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{1}{4}x + 2\), the y - intercept \(b = 2\). So, the line crosses the y - axis at the point \((0,2)\).

Step2: Use the slope to find another point

The slope \(m=\frac{1}{4}\), which means for every 4 units we move to the right (increase in \(x\) by 4), we move up 1 unit (increase in \(y\) by 1). Starting from the y - intercept \((0,2)\), if we move \(x = 4\) (from \(x = 0\) to \(x=4\)), then \(y=2 + 1=3\). So, another point on the line is \((4,3)\).

Step3: Plot the points and draw the line

Plot the points \((0,2)\) and \((4,3)\) on the coordinate plane. Then, draw a straight line passing through these two points.

(If the problem was to graph the line, this is the process. If it was to find some other property, like slope or intercept, we can extract that from the equation as well. For example, slope \(m=\frac{1}{4}\), y - intercept \(b = 2\))

Answer:

If graphing: The line is graphed by plotting \((0,2)\) and \((4,3)\) (or other points using the slope) and drawing a line through them. If finding slope: \(\frac{1}{4}\), if finding y - intercept: \(2\) (depending on the actual question, but since the problem was not fully specified, but the equation is \(y = \frac{1}{4}x+2\), key features are slope \(\frac{1}{4}\) and y - intercept \(2\))