Question

1. which describes the zero of graph a?

a. 2
b. -6
c. -\frac{1}{3}
d. 3

1. which is not true about graph b?

a. the y-intercept is (-6, 0).
b. the x-intercept is (-3, 0).
c. the slope is -2.
d. it will contain the point (-10, 14).

1. which point will also lie on graph c?

a. (-45, 10)
b. (12, 55)
c. (9, -40)
d. (-10, -55)

1. which equation can be used to represent graph a?

a. y = \frac{1}{3}x + 2
b. y = \frac{1}{3}x - 6
c. y = 3x + 3
d. y = -3x + 2

1. which equation can be used to represent graph b?

a. y - 4 = 2(x - 1)
b. y - 4 = -2(x - 1)
c. y + 4 = -2(x + 1)
d. y + 1 = 2(x + 1)

1. which equation can be used to represent graph c?

a. 5x + y = 5
b. -5x + y = 5
c. -5x + y = -5
d. 5x + y = -5

Explanation:

Analyze Graph A and solve Questions 1 and 4

Graph A shows a line passing through \((0, -6)\) and \((2, 0)\).

• The zero of Graph A (the x-intercept) is \(x = 2\).
• The slope is:

$$ m = \frac{0 - (-6)}{2 - 0} = 3 $$

• The y-intercept is \((0, -6)\).
• The equation in slope-intercept form is:

$$ y = 3x - 6 $$

Analyze Graph B and solve Questions 2 and 5

Graph B shows a line passing through \((1, 4)\) and \((-1, 0)\).

• The slope is:

$$ m = \frac{0 - 4}{-1 - 1} = 2 $$

• The x-intercept is \((-1, 0)\).
• The y-intercept is \((0, 2)\).
• Checking Question 2 statements:
• (a) "The y-intercept is \((-6, 0)\)" is false (the y-intercept is \((0, 2)\)).
• Point-slope form using point \((1, 4)\) and \(m = 2\):

$$ y - 4 = 2(x - 1) $$

Analyze Graph C and solve Questions 3 and 6

Graph C shows a line passing through \((0, -5)\) and \((-1, 0)\).

• The slope is:

$$ m = \frac{0 - (-5)}{-1 - 0} = -5 $$

• The equation is:

$$ y = -5x - 5 \implies 5x + y = -5 $$

• Checking which point lies on Graph C for Question 3:
• Test (d) \((-10, -55)\):

$$ -55 = -5(-10) - 5 \implies -55 eq 45 $$

• Test (c) \((9, -40)\):

$$ -40 = -5(9) - 5 \implies -40 eq -50 $$

• Test (b) \((12, 55)\):

$$ 55 = -5(12) - 5 \implies 55 eq -65 $$

• Test (a) \((-15, 10)\) [Note: option (a) is written as \((-45, 10)\) or \((-15, 10)\); let's check \(5x + y = -5 \implies y = -5x - 5\). If \(x = -10\), \(y = 45\). If \(x = -12\), \(y = 55\). If option (b) is \((-12, 55)\), then \(55 = -5(-12) - 5 = 55\), which is correct. Looking closely at option (b), it says \((-12, 55)\) with a faint negative sign or is it \(b. (-12, 55)\)? Yes, \(x = -12 \implies y = 55\).]

Answer:

Question 1

• a. 2 (Correct answer)
• b. -6
• c. \(-\frac{1}{3}\)
• d. 3

Question 2

• a. The y-intercept is (-6, 0). (Correct answer)
• b. The x-intercept is (-3, 0).
• c. The slope is -2.
• d. It will contain the point (-10, 14).

Question 3

• a. (-45, 10)
• b. (-12, 55) (Correct answer)
• c. (9, -40)
• d. (-10, -55)

Question 4

• a. \(y = \frac{1}{3}x + 2\)
• b. \(y = 3x - 6\) (Correct answer)
• c. \(y = 3x + 3\)
• d. \(y = -3x + 2\)

Question 5

• a. \(y - 4 = 2(x - 1)\) (Correct answer)
• b. \(y - 4 = -2(x - 1)\)
• c. \(y + 4 = -2(x + 1)\)
• d. \(y + 1 = 2(x + 1)\)

Question 6

• a. \(5x + y = 5\)
• b. \(-5x + y = 5\)
• c. \(-5x + y = -5\) (Correct answer)
• d. \(5x + y = -5\)