The equation you provided, $p = -0.03x + 90$, represents a linear supply or demand curve, where:

• $p$ is the price,
• $x$ is the quantity, and
• The equation is in slope-intercept form: $p = mx + b$, where $m = -0.03$ is the slope and $b = 90$ is the y-intercept.

Interpreting the Equation

• Slope ($-0.03$): This indicates that for every increase of 1 unit in $x$ (quantity), the price decreases by 0.03 units.
• Y-intercept ($90$): When $x = 0$, the price is 90.

To graph the equation:

We need to find a few points by choosing different values of $x$ and calculating $p$.

Let's calculate the following points:

1. For $x = 0$: $p = -0.03(0) + 90 = 90$ So, the point is $(0, 90)$.

2. For $x = 10$: $p = -0.03(10) + 90 = 90 - 0.3 = 89.7$ So, the point is $(10, 89.7)$.

3. For $x = 20$: $p = -0.03(20) + 90 = 90 - 0.6 = 89.4$ So, the point is $(20, 89.4)$.

4. For $x = 30$: $p = -0.03(30) + 90 = 90 - 0.9 = 89.1$ So, the point is $(30, 89.1)$.

5. For $x = 40$: $p = -0.03(40) + 90 = 90 - 1.2 = 88.8$ So, the point is $(40, 88.8)$.

Points on the Graph:

• $(0, 90)$
• $(10, 89.7)$
• $(20, 89.4)$
• $(30, 89.1)$
• $(40, 88.8)$

These points give a straight line when plotted, showing a downward-sloping curve, which typically represents a demand curve (as price decreases with an increase in quantity).

Would you like me to graph this for you or provide further explanations? Also, let me know if you have questions about this or would like more detail on how to graph equations!

Related Questions:

1. How would the graph change if the slope were positive instead of negative?
2. How do you find the equilibrium point between supply and demand curves?
3. What does the intercept value mean in terms of price and quantity?
4. How do you convert this linear equation to a different form, like standard form?
5. What happens if the slope is steeper or shallower?

Tip:

When graphing linear equations, remember that the slope indicates how steep the line is, and the y-intercept shows where the line crosses the price axis.