Question

graph the line that passes through the points (3, 2) and (6, 7) 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((3, 2)\) and \((6, 7)\), we have \( x_1 = 3, y_1 = 2, x_2 = 6, y_2 = 7 \). So, \( m=\frac{7 - 2}{6 - 3}=\frac{5}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((3, 2)\) and \( m=\frac{5}{3} \), we get \( y - 2=\frac{5}{3}(x - 3) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 2=\frac{5}{3}x-5 \). Then, add 2 to both sides: \( y=\frac{5}{3}x - 5 + 2=\frac{5}{3}x-3 \).
To graph the line, plot the points \((3, 2)\) and \((6, 7)\) on the coordinate plane and draw a straight line passing through them.

Answer:

The equation of the line is \( y=\frac{5}{3}x - 3 \)