Question

Use the table to find the slope and y-intercept of the line and then write the equation in slope intercept form. You must show ALL work to earn full credit.

x=-5,0,5,10
y=4,1,-2,-5

Answer 1

To find the slope and y-intercept of the line represented by the points in the table, we will first use the coordinates provided.

The points based on the table are:
- (-5, 4)
- (0, 1)
- (5, -2)
- (10, -5)

### Step 1: Find the Slope (m)

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's take two points: (-5, 4) and (0, 1).

Here,
- \( x_1 = -5 \), \( y_1 = 4 \)
- \( x_2 = 0 \), \( y_2 = 1 \)

Now substitute these values into the slope formula:

\[
m = \frac{1 - 4}{0 - (-5)} = \frac{1 - 4}{0 + 5} = \frac{-3}{5}
\]

Thus, the slope \( m = -\frac{3}{5} \).

### Step 2: Find the y-intercept (b)

To find the y-intercept, we can use the point where \( x = 0 \). From the table, when \( x = 0 \), \( y = 1 \). This point \((0, 1)\) gives us the y-intercept directly.

So:
- The y-intercept \( b = 1 \).

### Step 3: Write the Equation in Slope-Intercept Form

The slope-intercept form of a linear equation is given by:

\[
y = mx + b
\]

Substituting the values we found:

\[
y = -\frac{3}{5}x + 1
\]

### Final Answer

The slope is \( -\frac{3}{5} \) and the y-intercept is \( 1 \). The equation of the line in slope-intercept form is:

\[
\boxed{y = -\frac{3}{5}x + 1}
\]