Fill in the blanks below.Find the slope of the line passing through the points 4, 5 and −4, 7.slope: Find the slope of the line passing through the points −3, 9 and 9, 9.slope: Undefined

Sure, let's find the slopes step by step.

Slope of the line passing through the points (4, 5) and (−4, 7):

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

For the points (4, 5) and (−4, 7):

• $x_1 = 4$
• $y_1 = 5$
• $x_2 = -4$
• $y_2 = 7$

Plugging these values into the formula: $m = \frac{7 - 5}{-4 - 4} = \frac{2}{-8} = -\frac{1}{4}$

So, the slope of the line passing through the points (4, 5) and (−4, 7) is: $\text{slope: } -\frac{1}{4}$

Slope of the line passing through the points (−3, 9) and (9, 9):

For the points (−3, 9) and (9, 9):

• $x_1 = -3$
• $y_1 = 9$
• $x_2 = 9$
• $y_2 = 9$

Plugging these values into the formula: $m = \frac{9 - 9}{9 - (-3)} = \frac{0}{12} = 0$

So, the slope of the line passing through the points (−3, 9) and (9, 9) is: $\text{slope: } 0$

Summary:

• The slope of the line passing through the points (4, 5) and (−4, 7) is $-\frac{1}{4}$.
• The slope of the line passing through the points (−3, 9) and (9, 9) is $0$.