Question

1. what is the equation in point - slope form of the line that passes through (-7, 1) and (-3, 9)?

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, \((x_1,y_1)=(-7,1)\) and \((x_2,y_2)=(-3,9)\). So, \( m=\frac{9 - 1}{-3-(-7)}=\frac{8}{4} = 2 \).

Step2: Use 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 \((-7,1)\). Substituting \( m = 2 \), \( x_1=-7 \) and \( y_1 = 1 \) into the formula, we get \( y - 1=2(x+7) \). We could also use the point \((-3,9)\), and we would get \( y - 9=2(x + 3) \).

Answer:

\( y - 1=2(x + 7) \) (or \( y - 9=2(x + 3) \))