Question

question
what is an equation of the line that passes through the points (-3,8) and (6,2)?
answer attempt 1 out of 2

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, \( (x_1, y_1)=(-3, 8) \) and \( (x_2, y_2)=(6, 2) \). So, \( m=\frac{2 - 8}{6 - (-3)}=\frac{-6}{9}=-\frac{2}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \( (-3, 8) \). Substitute \( m = -\frac{2}{3} \), \( x_1=-3 \), and \( y_1 = 8 \) into the formula:
\( y - 8=-\frac{2}{3}(x - (-3)) \)
\( y - 8=-\frac{2}{3}(x + 3) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 8=-\frac{2}{3}x-2 \)
Add 8 to both sides: \( y=-\frac{2}{3}x + 6 \)
We can also write it in standard form \( 2x+3y = 18 \) (by multiplying both sides by 3: \( 3y=-2x + 18 \), then \( 2x + 3y=18 \))

Answer:

One equation of the line is \( y = -\frac{2}{3}x+6 \) (or \( 2x + 3y = 18 \))