Interpretation: See solution. Paint Bottles: 6 Justification: See solution.
Practice makes perfect
We have 30 dollars to spend on paint and clay. The given equation represents this situation.
2x+6y=30
Here, x represents the number of paint bottles and y is the number of tubs of clay. To graph this equation, we will start by finding the y-intercept. Remember that the y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. This will occurs when x=0.
The y-intercept is equal to 5, which means that one point on the line is (0,5). Now, we will find the x-intercept. Recall that the x-intercept is the x-coordinate of the point where the line crosses the x-axis. It occurs when y=0.
This means that another point on the line is (15,0). Let's plot the points in a coordinate plane and connect them with a line to obtain the graph of the given equation.
The y-intercept represents the number of tubs of clay that we can buy if we do not buy any paint. Similarly, the x-intercept gives us the number of paint bottles that we can buy if we do not buy any clay. Now, we want to find the number of paint bottles that we can buy if we buy 3 tubs of clay. To do so, will substitute y= 3 into the given equation.
2x+6( 3)=30
Finally, let's solve this equation for x!
