Question

in slope-intercept form, what is the equation of the line containing the points (-2, 5) and (4, -1)?
○ y = -x + 3
○ y = -x + 1
○ y = -3x + 1
○ y = x + 3

Explanation:

Step1: Calculate 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, \( x_1=-2,y_1 = 5,x_2=4,y_2=-1 \). So \( m=\frac{-1 - 5}{4-(-2)}=\frac{-6}{6}=-1 \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-2,5)\) and \( m=-1 \), we have \( y - 5=-1(x + 2) \).

Step3: Simplify to slope - intercept form

Simplify \( y - 5=-x - 2 \), add 5 to both sides: \( y=-x - 2 + 5=-x+3 \). We can also check by plugging the points into the options. For \((-2,5)\):

• For \( y=-x + 3 \), when \( x=-2 \), \( y=-(-2)+3=2 + 3 = 5 \), which matches.
• For \( y=-x + 1 \), when \( x=-2 \), \( y=-(-2)+1=3

eq5 \).

• For \( y=-3x + 1 \), when \( x=-2 \), \( y=-3\times(-2)+1 = 7

eq5 \).

• For \( y=x + 3 \), when \( x=-2 \), \( y=-2 + 3 = 1

eq5 \).

Answer:

A. \( y=-x + 3 \)