To determine the equation of the line that passes through the points (-3, -2) and (1, 6), we follow these steps:
1. Identify the coordinates:
- Point 1 (x₁, y₁) = (-3, -2)
- Point 2 (x₂, y₂) = (1, 6)
2. Calculate the slope (m):
The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]\[
m = \frac{y₂ - y₁}{x₂ - x₁}
\][/tex]
Plugging in the given points:
[tex]\[
m = \frac{6 - (-2)}{1 - (-3)} = \frac{6 + 2}{1 + 3} = \frac{8}{4} = 2.0
\][/tex]
Thus, the slope [tex]\( m = 2.0 \)[/tex].
3. Determine the y-intercept (b):
The equation of a line in slope-intercept form is [tex]\( y = mx + b \)[/tex]. To find the y-intercept, we can use one of the points and solve for [tex]\( b \)[/tex]. Let’s use point (-3, -2):
[tex]\[
y = mx + b \implies -2 = 2.0(-3) + b
\][/tex]
Simplify and solve for [tex]\( b \)[/tex]:
[tex]\[
-2 = -6 + b \implies b = -2 + 6 \implies b = 4.0
\][/tex]
4. Write the equation of the line:
The equation of the line in slope-intercept form [tex]\( y = mx + b \)[/tex] with the slope [tex]\( m = 2.0 \)[/tex] and y-intercept [tex]\( b = 4.0 \)[/tex] is given by:
[tex]\[
y = 2.0x + 4.0
\][/tex]
Hence, the equation of the line that passes through the points (-3, -2) and (1, 6) is:
[tex]\[
\boxed{y = 2.0x + 4.0}
\][/tex]
