write an equation in slope-intercept form for the line with slope -8 and y-intercept 7. then graph the line

Answer 1

To write the equation of a line in slope-intercept form, we use the formula:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

Given that the slope \( m = -8 \) and the y-intercept \( b = 7 \), we can substitute these values into the equation:

\[ y = -8x + 7 \]

Now, let's graph the line.

1. Plot the y-intercept: Start by marking the point (0, 7) on the y-axis.

2. Use the slope to find another point: The slope \( -8 \) means that for every 1 unit you move to the right (positive direction on the x-axis), you move 8 units down (negative direction on the y-axis). From the point (0, 7), if you move 1 unit to the right (to \( x = 1 \)), you would go down 8 units, landing at the point (1, -1).

3. Plot more points: From (1, -1), if you go another unit right to \( x = 2 \), you would go down an additional 8 units to \( y = -9 \), landing at (2, -9).

4. Draw the line: Connect the points you've plotted with a straight line extending in both directions.

Summary of the points:

• Y-intercept: (0, 7)
• Second point: (1, -1)
• Third point: (2, -9)

This creates a line with the equation:

\[ y = -8x + 7 \]

Graph Representation: While I can't create a visual graph directly in this text environment, you can sketch it using the points provided. The line will have a steep downward slope as it moves from left to right. If you have graphing software or graph paper, you can use these points to get a precise representation of the line.

Answer 2

find the y-intercept and slope of the graph
x 0 1 2 3 4
y 7 5 3 1 -1

Answer 3

To find the slope and the y-intercept from the given points, you can start by identifying two points on the graph:

From the data you've provided, we have the following points:

• (0, 7)
• (1, 5)
• (2, 3)
• (3, 1)
• (4, -1)

Step 1: Find the slope

The slope \( m \) can be calculated using the formula:

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

Let's take two points: (0, 7) and (1, 5).

• \( (x_1, y_1) = (0, 7) \)
• \( (x_2, y_2) = (1, 5) \)

Substituting into the slope formula:

\[ m = \frac{5 - 7}{1 - 0} = \frac{-2}{1} = -2 \]

Step 2: Find the y-intercept

The y-intercept is the value of \( y \) when \( x = 0 \). From the points given, when \( x = 0 \), \( y = 7 \). Therefore, the y-intercept \( b = 7 \).

Summary

• Slope (m): -2
• Y-intercept (b): 7

Thus, the equation of the line in slope-intercept form is:

\[ y = -2x + 7 \]

The y-intercept is at the point (0, 7), and the slope indicates that for every 1 unit increase in \( x \), \( y \) decreases by 2 units.

Answer 4

find the equation of the line with the plots
(-6, 3)
(4, -5)

Answer 5

To find the equation of the line that passes through the points \((-6, 3)\) and \((4, -5)\), we can follow these steps:

Step 1: Calculate the slope (m)

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

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

Using the points:

• \((x_1, y_1) = (-6, 3)\)
• \((x_2, y_2) = (4, -5)\)

Substituting in the values:

\[ m = \frac{-5 - 3}{4 - (-6)} = \frac{-8}{4 + 6} = \frac{-8}{10} = -\frac{4}{5} \]

Step 2: Use the slope-intercept form

The general slope-intercept form of a line is:

\[ y = mx + b \]

We have the slope \( m = -\frac{4}{5} \). Next, we can use one of the points to find the y-intercept \( b \). Let's use the point \((-6, 3)\):

Substituting \( x = -6 \) and \( y = 3 \) into the equation:

\[ 3 = -\frac{4}{5}(-6) + b \]

Calculating the term on the right:

\[ 3 = \frac{24}{5} + b \]

Now, isolate \( b \):

\[ b = 3 - \frac{24}{5} \]

Convert 3 to a fraction with a denominator of 5:

\[ b = \frac{15}{5} - \frac{24}{5} = \frac{15 - 24}{5} = \frac{-9}{5} \]

Step 3: Write the equation

Now we have:

• Slope \( m = -\frac{4}{5} \)
• Y-intercept \( b = -\frac{9}{5} \)

Thus, the equation of the line in slope-intercept form is:

\[ y = -\frac{4}{5}x - \frac{9}{5} \]

Summary

The equation of the line that passes through the points \((-6, 3)\) and \((4, -5)\) is:

\[ y = -\frac{4}{5}x - \frac{9}{5} \]