Question

The amount of money a student spends at the end of year carnival can be represented by the given equation. Graph the equation on the coordinate plane.

Answer 1

Answer: See the graph attached.

Explanation:

The Slope-intercept form of the equation of the line is:

`y=mx+b`

Where "m" is the slope and "b" is the intersection of the line with the y-axis.

Given the equation
`y=(1)/(2)x+3`, you can identify that:

`m=(1)/(2)\\\\b=3`

The line intercepts the y-axis when
`x=0`, therefore, you can know that the line passes through the point:

(0,3) → Point of intersection with the y-axis.

Now, substitute
`y=0` and solve for "x" to find the point of intersection with the x-axis:

`0=(1)/(2)x+3\\\\-3=(1)/(2)x\\\\(-3)(2)=x\\\\x=-6`

Now, you know that the line also passes through the point:

(-6,0) → Point of intersection with the x-axis.

Draw the a line that passes through these points.

Therefore, you get the graph attached.