To complete the equation of the line through the points [tex]\((-6, -5)\)[/tex] and [tex]\((-4, -4)\)[/tex], we will follow these steps:
1. Calculate the slope [tex]\( m \)[/tex]:
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points into the formula:
[tex]\[
m = \frac{-4 - (-5)}{-4 - (-6)} = \frac{-4 + 5}{-4 + 6} = \frac{1}{2} = 0.5
\][/tex]
2. Determine the y-intercept [tex]\( b \)[/tex]:
Use the slope-intercept form of the line equation, which is [tex]\( y = mx + b \)[/tex]. Substitute one of the points [tex]\((-6, -5)\)[/tex] into this equation along with the slope [tex]\( m = 0.5 \)[/tex]:
[tex]\[
-5 = 0.5 \cdot (-6) + b
\][/tex]
Simplify to solve for [tex]\( b \)[/tex]:
[tex]\[
-5 = -3 + b \implies b = -5 + 3 \implies b = -2
\][/tex]
3. Write the equation of the line:
Now that we have the slope [tex]\( m = 0.5 \)[/tex] and the y-intercept [tex]\( b = -2 \)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[
y = 0.5x - 2
\][/tex]
So, the complete equation of the line is:
[tex]\[
y = 0.5x - 2
\][/tex]
