Question

graph the line that passes through the points (8, 4) and (2, 7) and determine the equation of the line.

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(8, 4)\) and \((x_2, y_2)=(2, 7)\). Then \(m=\frac{7 - 4}{2 - 8}=\frac{3}{-6}=-\frac{1}{2}\).

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 \(m =-\frac{1}{2}\). Substitute into the formula: \(y - 4=-\frac{1}{2}(x - 8)\).

Step3: Simplify the equation

Expand the right - hand side: \(y - 4=-\frac{1}{2}x+4\). Then add 4 to both sides: \(y=-\frac{1}{2}x + 8\).

(For graphing: Plot the points \((8, 4)\) and \((2, 7)\) on the coordinate plane. Then draw a straight line passing through these two points. The line should have a slope of \(-\frac{1}{2}\) and a y - intercept of 8.)

Answer:

The equation of the line is \(y =-\frac{1}{2}x + 8\). To graph the line, plot the points \((8, 4)\) and \((2, 7)\) and draw a straight line through them.