Question

1. a line passes through the points (-3, 2) and (3, 8). write its equation in slope - intercept form.
2. write your answer using integers, proper fractions, and improper fractions in simplest form.

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, \( (x_1, y_1)=(-3, 2) \) and \( (x_2, y_2)=(3, 8) \). So, \( m=\frac{8 - 2}{3 - (-3)}=\frac{6}{6} = 1 \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((-3, 2)\) and \( m = 1 \), we have \( y - 2=1\times(x - (-3)) \), which simplifies to \( y - 2=x + 3 \).

Step3: Convert to slope - intercept form

Slope - intercept form is \( y=mx + b \). From \( y - 2=x + 3 \), add 2 to both sides: \( y=x+3 + 2 \), so \( y=x + 5 \).

Answer:

\( y = x+5 \)