Use the following information to answer Questions 3-4.

[tex]\[
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & -8 \\
\hline
-1 & 2 \\
\hline
2 & 17 \\
\hline
5 & 32 \\
\hline
\end{tabular}
\][/tex]

3. What is the [tex]$y$[/tex]-intercept?

4. Write an equation in standard form.



Answer :

Certainly! Let's solve these questions step by step.

### Question 3: What is the \( y \)-intercept?

To find the \( y \)-intercept of a line that passes through the given points, we first need to determine the equation of the line in the slope-intercept form, \( y = mx + c \), where \( m \) is the slope and \( c \) is the \( y \)-intercept.

#### 1. Calculate the slope (\( m \))

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Using the first two points \((-3, -8)\) and \((-1, 2)\):
[tex]\[ m = \frac{2 - (-8)}{-1 - (-3)} = \frac{2 + 8}{-1 + 3} = \frac{10}{2} = 5 \][/tex]

So, the slope \( m \) is \( 5 \).

#### 2. Calculate the \( y \)-intercept (\( c \))

We can use the slope-intercept form \( y = mx + c \) to find the \( y \)-intercept \( c \). Using one of the points, for example \((-3, -8)\), and substituting \( m = 5 \):

[tex]\[ -8 = 5(-3) + c \][/tex]

Solving for \( c \):
[tex]\[ -8 = -15 + c \][/tex]
[tex]\[ c = -8 + 15 \][/tex]
[tex]\[ c = 7 \][/tex]

Therefore, the \( y \)-intercept \( c \) is \( 7 \).

### Question 4: Write an equation in standard form.

The standard form of the equation of a line is \( Ax + By = C \). We already have the slope-intercept form as \( y = 5x + 7 \).

To convert this equation to standard form:

1. Move all terms to one side of the equation to set it equal to \( 0 \):
[tex]\[ y - 5x - 7 = 0 \][/tex]

2. Rearrange it to match \( Ax + By = C \):
[tex]\[ 5x - y = -7 \][/tex]

Thus, the equation in standard form is:
[tex]\[ 5x - y = -7 \][/tex]

### Summary
To answer the questions:
3. The \( y \)-intercept is \( 7 \).
4. The equation in standard form is [tex]\( 5x - y = -7 \)[/tex].