Question

4)
equation
ordered pair = (-4,-3)
ordered pair = (4,1)
slope (m) =
y-intercept = -1

Explanation:

Step1: Recall 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, \((x_1,y_1)=(-4,-3)\) and \((x_2,y_2)=(4,1)\).

Step2: Substitute values into slope formula

Substitute \( x_1=-4,y_1 = - 3,x_2 = 4,y_2=1 \) into the formula: \( m=\frac{1-(-3)}{4-(-4)}=\frac{1 + 3}{4 + 4}=\frac{4}{8}=\frac{1}{2} \).

Step3: Recall slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know \( m=\frac{1}{2} \) and \( b=-1 \).

Step4: Write the equation

Substitute \( m=\frac{1}{2} \) and \( b = - 1 \) into \( y=mx + b \), we get \( y=\frac{1}{2}x-1 \).

Answer:

• Slope (\( m \)): \(\frac{1}{2}\)
• Equation: \( y=\frac{1}{2}x - 1 \)