Question

1. write the point slope equation of the line that passes through (-3, -3) and (1, 5). (10 pts)

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, \((x_1,y_1)=(-3,-3)\) and \((x_2,y_2)=(1,5)\). So, \( m=\frac{5 - (-3)}{1 - (-3)}=\frac{5 + 3}{1 + 3}=\frac{8}{4}=2 \).

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 \((-3,-3)\) with \( m = 2 \), \( x_1=-3 \) and \( y_1=-3 \). Substituting these values into the point - slope formula, we get \( y-(-3)=2(x - (-3)) \), which simplifies to \( y + 3=2(x + 3) \). We could also use the point \((1,5)\): \( y - 5=2(x - 1) \).

Answer:

\( y + 3 = 2(x + 3) \) (or \( y - 5 = 2(x - 1) \))