Question

2
a line in the xy-plane passes through the points (0, 2) and (1, -3).
which of the following is an equation of this line?
a ( y = 5x + 2 )
b ( y = -5x + 2 )
c ( y = x + 2 )
d ( y = -x + 2 )

Explanation:

Step1: Find the slope

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, \((x_1, y_1)=(0, 2)\) and \((x_2, y_2)=(1, - 3)\). So \( m=\frac{-3 - 2}{1 - 0}=\frac{-5}{1}=-5 \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y = mx + b \), where \( b \) is the y - intercept. The line passes through \((0, 2)\), so when \( x = 0 \), \( y=2 \). Substituting \( x = 0 \), \( y = 2 \) and \( m=-5 \) into \( y=mx + b \), we get \( 2=-5\times0 + b \), so \( b = 2 \).

Step3: Write the equation

Substituting \( m=-5 \) and \( b = 2 \) into \( y=mx + b \), the equation of the line is \( y=-5x + 2 \).

Answer:

B. \( y=-5x + 2 \)