Question

question
graph the line with the equation $y = \frac{1}{2}x + 5$.

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{1}{2}x + 5\), \(b = 5\). So the line crosses the y - axis at the point \((0,5)\). Plot the point \((0,5)\) on the coordinate plane.

Step2: Use the slope to find another point

The slope \(m=\frac{1}{2}\), which means for every 2 units we move to the right (increase in \(x\) by 2), we move up 1 unit (increase in \(y\) by 1). Starting from \((0,5)\), if we move \(x = 2\) (so \(x\) becomes \(0 + 2=2\)) and \(y=5 + 1 = 6\), we get the point \((2,6)\). We can also move in the opposite direction: for \(x=- 2\) (decrease \(x\) by 2), \(y = 5-1=4\), so the point \((-2,4)\) is also on the line.

Step3: Draw the line

Connect the points (e.g., \((0,5)\) and \((2,6)\) or other points found using the slope) with a straight line. This line represents the equation \(y=\frac{1}{2}x + 5\).

Answer:

The line is graphed by first plotting the y - intercept \((0,5)\) and then using the slope \(\frac{1}{2}\) to find additional points (such as \((2,6)\) or \((-2,4)\)) and drawing a straight line through these points.