Question

the points (7, 3) and (9, 10) fall on a particular line. what is its equation in point - slope form? use one of the specified points in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

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 \((7, 3)\) and \((9, 10)\), we have \( x_1 = 7,y_1 = 3,x_2=9,y_2 = 10 \). So \( m=\frac{10 - 3}{9 - 7}=\frac{7}{2} \).

Step2: Recall point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use either of the two points. Let's use the point \((7, 3)\) (we could also use \((9,10)\)). Substituting \( m=\frac{7}{2} \), \( x_1 = 7 \) and \( y_1 = 3 \) into the point - slope formula, we get \( y - 3=\frac{7}{2}(x - 7) \). If we use the point \((9,10)\), substituting \( m = \frac{7}{2}\), \(x_1=9\) and \(y_1 = 10\) into the formula, we get \(y - 10=\frac{7}{2}(x - 9)\).

Answer:

\(y - 3=\frac{7}{2}(x - 7)\) (or \(y - 10=\frac{7}{2}(x - 9)\))