Question

line cd passes through points c(3, -5) and d(6, 0). what is the equation of line cd in standard form?
○ 5x + 3y = 18
○ 5x - 3y = 30
○ 5x - y = 30
○ 5x + y = 18

Explanation:

Step1: Find the slope of line CD

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \( C(3,-5) \) and \( D(6,0) \), we have \( x_1 = 3,y_1=-5,x_2 = 6,y_2 = 0 \). So \( m=\frac{0-(-5)}{6 - 3}=\frac{5}{3} \)? Wait, no, wait: \( 0-(-5)=5 \), \( 6 - 3 = 3 \)? Wait, no, wait, let's recalculate. Wait, \( y_2 - y_1=0-(-5)=5 \), \( x_2 - x_1=6 - 3 = 3 \)? Wait, no, that's wrong. Wait, the slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). So \( y_2=0 \), \( y_1=-5 \), so \( 0 - (-5)=5 \). \( x_2=6 \), \( x_1=3 \), so \( 6 - 3=3 \). Wait, but then let's use point - slope form. Wait, maybe I made a mistake. Wait, let's check the answer options. Let's use the two - point form of a line. The two - point form is \( y - y_1=m(x - x_1) \), where \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Wait, alternatively, we can plug the points into the given equations to see which one satisfies both points.

Let's check point \( C(3,-5) \) and \( D(6,0) \) in each equation.

First equation: \( 5x+3y = 18 \)

For \( C(3,-5) \): Left - hand side (LHS) \(=5\times3+3\times(-5)=15 - 15 = 0
eq18 \). So this equation is not correct.

Second equation: \( 5x-3y = 30 \)

For \( C(3,-5) \): LHS \(=5\times3-3\times(-5)=15 + 15 = 30 \). For \( D(6,0) \): LHS \(=5\times6-3\times0 = 30-0 = 30 \). Both points satisfy this equation. Let's check the other equations to be sure.

Third equation: \( 5x - y=30 \)

For \( C(3,-5) \): LHS \(=5\times3-(-5)=15 + 5 = 20
eq30 \). So this is wrong.

Fourth equation: \( 5x + y=18 \)

For \( C(3,-5) \): LHS \(=5\times3+(-5)=15 - 5 = 10
eq18 \). So this is wrong.

Answer:

B. \( 5x - 3y = 30 \)