Sure, let's go through the given equation step-by-step and solve for the slope, y-intercept, and x-intercept.
The given equation is:
[tex]\[ y - (-7) = 3(x - (-4)) \][/tex]
### Step 1: Simplify the Equation
First, we simplify the given equation:
[tex]\[ y + 7 = 3(x + 4) \][/tex]
### Step 2: Expand the Right Side
Next, we expand the right side of the equation:
[tex]\[ y + 7 = 3x + 12 \][/tex]
### Step 3: Put into Slope-Intercept Form
Subtract 7 from both sides to put the equation into the slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = 3x + 5 \][/tex]
From this form, it's clear that:
- The slope ([tex]\( m \)[/tex]) of the line is [tex]\( 3 \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\( 5 \)[/tex].
### Step 4: Find the x-Intercept
To find the x-intercept, we set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = 3x + 5 \][/tex]
[tex]\[ 3x = -5 \][/tex]
[tex]\[ x = -\frac{5}{3} \][/tex]
### Summary
Based on our steps, we have:
- Slope: [tex]\( 3 \)[/tex]
- y-intercept: [tex]\( 5 \)[/tex]
- x-intercept: [tex]\(-\frac{5}{3} \approx -1.6666666666666667 \)[/tex]
Here is the filled table:
[tex]\[
\begin{tabular}{|l|l|}
\hline \multicolumn{2}{|c|}{$y-(-7)=3(x-(-4))$} \\
\hline \begin{tabular}{l}
Slope-intercept \\
form:
\end{tabular} & \( y = 3x + 5 \) \\
\hline Slope: & \(3\) \\
\hline y-intercept: & \(5\) \\
\hline x-intercept: & \(-\frac{5}{3} \approx -1.6666666666666667 \) \\
\hline
\end{tabular}
\][/tex]
