Answer:
To find the equation of the line passing through the points (-8,-4) and (-6,-1), we first need to find the slope (\(m\)) of the line using the formula:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
Let's use the points (-8,-4) and (-6,-1):
\[m = \frac{{-1 - (-4)}}{{-6 - (-8)}} = \frac{{3}}{{2}}\]
Next, we'll use the point-slope form of a linear equation, which is:
\[y - y_1 = m(x - x_1)\]
We'll choose one of the points to substitute, let's use (-8,-4):
\[y - (-4) = \frac{{3}}{{2}}(x - (-8))\]
Simplify the equation:
\[y + 4 = \frac{{3}}{{2}}(x + 8)\]
Multiply both sides by 2 to eliminate the fraction:
\[2y + 8 = 3(x + 8)\]
Distribute the 3:
\[2y + 8 = 3x + 24\]
Now, isolate \(y\):
\[2y = 3x + 16\]
\[y = \frac{{3x + 16}}{{2}}\]
So, the equation of the line in slope-intercept form is \(y = \frac{{3x + 16}}{{2}}\).
Explanation: