Question

question
graph the line that passes through the points (8, -4) and (-8, 8) 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, \((x_1, y_1)=(8, - 4)\) and \((x_2, y_2)=(-8, 8)\). So, \( m=\frac{8-(-4)}{-8 - 8}=\frac{12}{-16}=-\frac{3}{4} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((8, - 4)\) and \( m =-\frac{3}{4} \). Substituting these values, we get \( y-(-4)=-\frac{3}{4}(x - 8) \).
Simplify this equation:
\( y + 4=-\frac{3}{4}x+6 \)
Subtract 4 from both sides: \( y=-\frac{3}{4}x + 2 \).

To graph the line:

1. Plot the points \((8,-4)\) and \((-8,8)\) on the coordinate plane.
2. Draw a straight line passing through these two points.

Answer:

The equation of the line is \( y =-\frac{3}{4}x + 2 \). To graph the line, plot the points \((8,-4)\) and \((-8,8)\) and draw a straight line through them.