Question

1. graph the equation 60x + 15y = 600.

use the graph to define the key features of 60x + 15y = 600
key feature | description
end behavior | as x - values increase, y - values
|
x - intercept | the x - intercept is
y - intercept | the y - intercept is
slope |

Explanation:

Step1: Find x - intercept

To find the x - intercept, set \(y = 0\) in the equation \(60x+15y = 600\).
Substitute \(y = 0\) into the equation: \(60x+15(0)=600\), which simplifies to \(60x=600\).
Divide both sides by 60: \(x=\frac{600}{60} = 10\). So the x - intercept is \((10,0)\).

Step2: Find y - intercept

To find the y - intercept, set \(x = 0\) in the equation \(60x + 15y=600\).
Substitute \(x = 0\) into the equation: \(60(0)+15y=600\), which simplifies to \(15y = 600\).
Divide both sides by 15: \(y=\frac{600}{15}=40\). So the y - intercept is \((0,40)\).

Step3: Find the slope

We can rewrite the equation \(60x + 15y=600\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
First, solve for \(y\):
\(15y=- 60x + 600\)
Divide each term by 15: \(y=\frac{-60x + 600}{15}=-4x + 40\).
So the slope \(m=-4\).

Step4: Analyze end - behavior

The equation \(y=-4x + 40\) is a linear equation with a slope \(m=-4\) (negative slope).
For a linear function \(y = mx + b\), if \(m<0\), as \(x\) values increase, \(y\) values decrease.

Answer:

• x - intercept: The x - intercept is \(10\) (the point is \((10,0)\)).
• y - intercept: The y - intercept is \(40\) (the point is \((0,40)\)).
• Slope: The slope is \(- 4\).
• End Behavior: As \(x\) - values increase, \(y\) - values decrease.