Question

line cd passes through points c(1, 3) and d(4, -3). if the equation of the line is written in slope - intercept form, y = mx + b, what is the value of b?
options: -5, -2, 1, 5

Explanation:

Step1: Calculate the slope \( m \)

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \( C(1, 3) \) and \( D(4, - 3) \), we have \( x_1 = 1,y_1 = 3,x_2 = 4,y_2=-3 \).
So \( m=\frac{-3 - 3}{4 - 1}=\frac{-6}{3}=-2 \).

Step2: Use point - slope form to find the equation of the line

We know the slope \( m=-2 \) and we can use point \( C(1,3) \). The point - slope form of a line is \( y - y_1=m(x - x_1) \).
Substitute \( m=-2 \), \( x_1 = 1 \), \( y_1 = 3 \) into the formula: \( y - 3=-2(x - 1) \).

Step3: Convert to slope - intercept form (\( y=mx + b \))

Expand the right - hand side: \( y-3=-2x + 2 \).
Add 3 to both sides of the equation: \( y=-2x+2 + 3 \), so \( y=-2x + 5 \).
In the slope - intercept form \( y = mx + b \), comparing with \( y=-2x + 5 \), we can see that \( b = 5 \).

Answer:

\( 5 \)