Question

1. graph y = 2x + 3.
2. the line shown represents the balance y of ben’s lunch account. two days ago, he owed $1. what is an equation of the line in point - slope form? circle the letter of the correct answer.

a. y - 1 = 2(x + 2)
b. y + 1 = -2(x + 2)
c. y - 1 = -2(x - 2)
d. y + 1 = 2(x + 2)

1. what are the x - and y - intercepts of the graph of 5x + 8y = 20? graph the equation.

x - intercept:
y - intercept:

1. jake needs to buy 120 beverages for a party. what equation, in standard form, determines the numbers of 8 - packs of juice x and 12 - packs of water y that jake can buy. box in your answer.
2. select all the equations that represent lines that are perpendicular to the graph of 6x + 18y = 5. circle the letter of the correct answer.

a. y = 3x - 10
b. x = 3
c. y + 6 = 3(x - 15)
d. 3x + 9y = 8
e. 2x - 3y = 5

1. graph the equation 4x + 8y = 16. what is the slope of the graph?

slope:

Explanation:

Step1: Find two - point for graphing \(y = 2x+3\)

When \(x = 0\), \(y=2\times0 + 3=3\). When \(y = 0\), \(0=2x + 3\), then \(x=-\frac{3}{2}\). Plot \((0,3)\) and \((-\frac{3}{2},0)\) and draw a line.

Step2: Analyze the line for Ben's lunch balance

The slope of the given line is \(- 2\) (from the graph). Two days ago (\(x=-2\)), \(y = - 1\). The point - slope form is \(y - y_1=m(x - x_1)\), so \(y+1=-2(x + 2)\). The answer is B.

Step3: Find intercepts of \(5x + 8y=20\)

For \(x\) - intercept, set \(y = 0\): \(5x=20\), \(x = 4\). For \(y\) - intercept, set \(x = 0\): \(8y=20\), \(y=\frac{5}{2}\).

Step4: Form an equation for Jake's beverage purchase

The number of juice cans from \(x\) 8 - packs is \(8x\), and from \(y\) 12 - packs of water is \(12y\). The total number of beverages is 120, so the equation is \(8x + 12y=120\), which simplifies to \(2x+3y = 30\).

Step5: Determine perpendicular lines to \(6x + 18y=5\)

Rewrite \(6x + 18y=5\) as \(y=-\frac{1}{3}x+\frac{5}{18}\), the slope is \(-\frac{1}{3}\). Perpendicular lines have a slope of 3.

• For \(y = 3x-10\), slope is 3.
• \(x = 3\) is a vertical line, not perpendicular to a non - vertical line with slope \(-\frac{1}{3}\).
• For \(y + 6=3(x - 15)\), slope is 3.
• Rewrite \(3x + 9y=8\) as \(y=-\frac{1}{3}x+\frac{8}{9}\), not perpendicular.
• Rewrite \(2x-3y=5\) as \(y=\frac{2}{3}x-\frac{5}{3}\), not perpendicular.

The answers are A and C.

Step6: Graph \(4x + 8y=16\) and find slope

Rewrite as \(y=-\frac{1}{2}x + 2\). When \(x = 0\), \(y = 2\); when \(y = 0\), \(x = 4\). Plot \((0,2)\) and \((4,0)\) and draw a line. The slope is \(-\frac{1}{2}\).

Answer:

1. Graph with points \((0,3)\) and \((-\frac{3}{2},0)\) connected by a line.
2. B. \(y + 1=-2(x + 2)\)
3. \(x\) - intercept: 4; \(y\) - intercept: \(\frac{5}{2}\)
4. \(2x + 3y=30\)
5. A. \(y = 3x-10\), C. \(y + 6=3(x - 15)\)
6. Graph with points \((0,2)\) and \((4,0)\) connected by a line; slope: \(-\frac{1}{2}\)