Question

1. a) -5 b) $\frac{1}{5}$ c) -$\frac{1}{5}$ d) 5 13) a) -3 b) 3 c) $\frac{1}{3}$ d) -$\frac{1}{3}$

Explanation:

1. For question 11:

• # Explanation:
• ## Step1: Recall the slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's assume the two points on the line in question 11 are \((x_1,y_1)\) and \((x_2,y_2)\). By counting the grid - squares, if we move from the lower point to the upper point, we can see that for a change in \(x\) (run) of 1 unit, the change in \(y\) (rise) is 5 units.
\(m=\frac{\text{rise}}{\text{run}}\)

• ## Step2: Calculate the slope

Since the line is increasing (going up from left to right), the slope is positive. And since \(\text{rise} = 5\) and \(\text{run}=1\), \(m = 5\).

• # Answer:

D. 5

1. For question 13:

• # Explanation:
• ## Step1: Recall the slope - formula

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). By counting the grid - squares, if we move from one point to another on the line in question 13, for a change in \(x\) (run) of 3 units, the change in \(y\) (rise) is 1 unit.
\(m=\frac{\text{rise}}{\text{run}}\)

• ## Step2: Calculate the slope

Since the line is increasing (going up from left to right), the slope is positive. And since \(\text{rise}=1\) and \(\text{run} = 3\), \(m=\frac{1}{3}\).

• # Answer:

C. \(\frac{1}{3}\)

Answer:

1. For question 11:

• # Explanation:
• ## Step1: Recall the slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's assume the two points on the line in question 11 are \((x_1,y_1)\) and \((x_2,y_2)\). By counting the grid - squares, if we move from the lower point to the upper point, we can see that for a change in \(x\) (run) of 1 unit, the change in \(y\) (rise) is 5 units.
\(m=\frac{\text{rise}}{\text{run}}\)

• ## Step2: Calculate the slope

Since the line is increasing (going up from left to right), the slope is positive. And since \(\text{rise} = 5\) and \(\text{run}=1\), \(m = 5\).

• # Answer:

D. 5

1. For question 13:

• # Explanation:
• ## Step1: Recall the slope - formula

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). By counting the grid - squares, if we move from one point to another on the line in question 13, for a change in \(x\) (run) of 3 units, the change in \(y\) (rise) is 1 unit.
\(m=\frac{\text{rise}}{\text{run}}\)

• ## Step2: Calculate the slope

Since the line is increasing (going up from left to right), the slope is positive. And since \(\text{rise}=1\) and \(\text{run} = 3\), \(m=\frac{1}{3}\).

• # Answer:

C. \(\frac{1}{3}\)