Question

1. (2, -5) and (7, -5)

(partially visible: (\frac{y_1 - y_2}{x_1 - x_2}) -like formula)

1. ( left( \frac{1}{4}, \frac{2}{3}

ight) ) and ( (0, \frac{1}{3}) )

Explanation:

Problem 7: Find the slope between points \((2, -5)\) and \((7, -5)\)

Step1: Recall the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 2\), \(y_1=-5\), \(x_2 = 7\), \(y_2=-5\).

Step2: Substitute values into the formula

Substitute the values into the slope formula: \(m=\frac{-5-(-5)}{7 - 2}\)

Step3: Simplify the numerator and denominator

Simplify the numerator: \(-5-(-5)=-5 + 5=0\)
Simplify the denominator: \(7 - 2 = 5\)
So, \(m=\frac{0}{5}=0\)

Step1: Recall the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1=\frac{1}{4}\), \(y_1 = \frac{2}{3}\), \(x_2=0\), \(y_2=\frac{1}{3}\)

Step2: Substitute values into the formula

Substitute the values into the slope formula: \(m=\frac{\frac{1}{3}-\frac{2}{3}}{0-\frac{1}{4}}\)

Step3: Simplify the numerator and denominator

Simplify the numerator: \(\frac{1}{3}-\frac{2}{3}=\frac{1 - 2}{3}=\frac{-1}{3}\)
Simplify the denominator: \(0-\frac{1}{4}=-\frac{1}{4}\)

Step4: Divide the numerator by the denominator

\(m=\frac{-\frac{1}{3}}{-\frac{1}{4}}=\frac{1}{3}\times\frac{4}{1}=\frac{4}{3}\) (since dividing by a fraction is multiplying by its reciprocal)

Answer:

The slope is \(0\)

Problem 9: Find the slope between points \((\frac{1}{4},\frac{2}{3})\) and \((0,\frac{1}{3})\)