Question

1. equations of two lines are given:

\\(y = 3x - 1\\)
\\(y = -2x + 9\\)

a) graph both lines on the grid to the right.

b) what are the coordinates of the point of intersection?

1. solve the system of equations from question 5 using either substitution or elimination.

1. john is a salesman. he gets paid \\$500 every week, plus 15% of every sale he makes.

a) write an equation for determining his weekly pay.

b) use your equation to determine his weekly pay if his sales were \\$600.

c) use your equation to determine the amount of his sales if his weekly pay was \\$725.

Explanation:

Graphing the linear equations

Using the Slope-Intercept Form knowledge point

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Finding the point of intersection

Using the Graphical Intersection knowledge point

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Solving the system algebraically

Using the Systems of Linear Equations knowledge point

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Modeling John's weekly pay

We define the variables:
Let \(P\) represent the weekly pay in dollars.
Let \(S\) represent the total sales in dollars.

The base pay is a constant \$500.
The commission is 15% of sales, which is represented as \(0.15S\).

Thus, the linear equation is:

$$P = 0.15S + 500$$

Evaluating and solving the model

For part b, we substitute \(S = 600\):

$$P = 0.15(600) + 500 = 90 + 500 = 590$$

For part c, we substitute \(P = 725\) and solve for \(S\):

$$725 = 0.15S + 500$$

$$225 = 0.15S$$

$$S = \frac{225}{0.15} = 1500$$

Answer:

Question 5

a) The lines are plotted on the grid. The line \(y = 3x - 1\) passes through \((0, -1)\) and \((2, 5)\). The line \(y = -2x + 9\) passes through \((0, 9)\) and \((2, 5)\).

b) The coordinates of the point of intersection are \((2, 5)\).

Question 6

Using substitution:

$$3x - 1 = -2x + 9$$

$$5x = 10 \implies x = 2$$

Substitute \(x = 2\) back into the first equation:

$$y = 3(2) - 1 = 5$$

The solution is \((2, 5)\).

Question 7

a) \(P = 0.15S + 500\) (where \(P\) is the weekly pay and \(S\) is the sales amount)

b) His weekly pay is \$590.

c) The amount of his sales was \$1,500.