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[tex]\[
\begin{array}{|l|l|}
\hline
\multicolumn{2}{|c|}{y - (-7) = 3(x - (-4))} \\
\hline
\begin{array}{l}
\text{Slope-intercept form:}
\end{array} & \\
\hline
\text{Slope:} & \\
\hline
\text{y-intercept:} & \\
\hline
\text{x-intercept:} & \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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