Question

1. $y = \frac{1}{3}x - 5$ (and a coordinate grid for graphing)

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{1}{3}x - 5\), the slope \(m=\frac{1}{3}\) and the y - intercept \(b=- 5\).

Step2: Plot the y-intercept

The y - intercept is \(-5\), so we plot the point \((0,-5)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m = \frac{1}{3}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). From the point \((0,-5)\), we move up 1 unit (change in \(y = + 1\)) and then move to the right 3 units (change in \(x=+3\)). This gives us the point \((0 + 3,-5 + 1)=(3,-4)\). We can also move down 1 unit and left 3 units from \((0,-5)\) to get another point \((0-3,-5 - 1)=(-3,-6)\).

Step4: Draw the line

Draw a straight line through the points \((0,-5)\), \((3,-4)\) (or other points found using the slope) to graph the line \(y=\frac{1}{3}x-5\).

Answer:

The graph is a straight line with a y - intercept at \((0, - 5)\) and a slope of \(\frac{1}{3}\), passing through points like \((3,-4)\) and \((-3,-6)\) (or other points determined by the slope from the y - intercept).