Question

date: 1/15/25
find the missing value so that the ordered pairs
have the given slope.

1. $(x, -1)$ and $(-2, -3)$; $m = -dfrac{1}{2}$

1. $(-1, -9)$ and $(2, y)$; $m = 3$

Explanation:

Problem 1:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(x, - 1)\), \((x_2,y_2)=(-2,-3)\), and \( m =-\frac{1}{2} \). Substitute into the formula:
\( -\frac{1}{2}=\frac{-3 - (-1)}{-2 - x} \)

Step2: Simplify numerator

Simplify the numerator: \(-3-(-1)=-3 + 1=-2\). So the equation becomes:
\( -\frac{1}{2}=\frac{-2}{-2 - x} \)

Step3: Cross - multiply

Cross - multiply: \(-1\times(-2 - x)=2\times(-2)\)

Step4: Solve for x

Simplify both sides: \(2 + x=-4\). Subtract 2 from both sides: \(x=-4 - 2=-6\)

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(-1,-9)\), \((x_2,y_2)=(2,y)\), and \( m = 3 \). Substitute into the formula:
\( 3=\frac{y-(-9)}{2-(-1)} \)

Step2: Simplify denominator

Simplify the denominator: \(2-(-1)=2 + 1 = 3\). So the equation becomes:
\( 3=\frac{y + 9}{3} \)

Step3: Solve for y

Multiply both sides by 3: \(3\times3=y + 9\), which is \(9=y + 9\). Subtract 9 from both sides: \(y=9 - 9=0\)

Answer:

\( x=-6 \)

Problem 2: