Question

graph the line that passes through the points (-2, 5) and (-4, 3) and determine the equation of the line.

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, \((x_1, y_1)=(-2, 5)\) and \((x_2, y_2)=(-4, 3)\). So, \( m=\frac{3 - 5}{-4 - (-2)}=\frac{-2}{-2}=1 \).

Step2: Use point - slope form

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

Step3: Rewrite in slope - intercept form

Adding 5 to both sides of the equation \( y - 5=x + 2 \), we get \( y=x+7 \).

Answer:

The equation of the line is \( y = x + 7 \)