Question

A graph shows two points
a dot on 1 (y axis)
a dot on (3,-1)
What is the slope and y intercept

Answer 1

How about a graph showing
a dot on -2 (y axis)
a dot on (2,0)
What is the slope and y intercept

Answer 2

To find the slope and y-intercept using the given points, we can use the following information:

1. The first point is (0, 1), which means it is located on the y-axis at (0, 1). This gives us the y-intercept directly since it represents the point where the line crosses the y-axis.
2. The second point is (3, -1).

### Finding the Slope (m)

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

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

Using the points (0, 1) and (3, -1):

- \( (x_1, y_1) = (0, 1) \)
- \( (x_2, y_2) = (3, -1) \)

Substituting in these values:

\[
m = \frac{-1 - 1}{3 - 0} = \frac{-2}{3}
\]

So, the slope \( m = -\frac{2}{3} \).

### Finding the y-intercept (b)

The y-intercept is the value of \( y \) when \( x = 0 \). From the first point (0, 1), we can see that the y-intercept \( b = 1 \).

### Summary

- Slope (m): \( -\frac{2}{3} \)
- Y-intercept (b): \( 1 \)

The equation of the line can be expressed in slope-intercept form \( y = mx + b \):

\[
y = -\frac{2}{3}x + 1
\]

Answer 3

To find the slope and y-intercept using the given points, we need to identify the coordinates of the points.

1. The first point on the y-axis is (0, -2), which means it is located at (0, -2). This gives us the y-intercept directly since it represents the point where the line crosses the y-axis.
2. The second point is (2, 0).

### Finding the Slope (m)

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

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

Using the points (0, -2) and (2, 0):

- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (2, 0) \)

Substituting these values into the slope formula:

\[
m = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1
\]

So, the slope \( m = 1 \).

### Finding the y-intercept (b)

The y-intercept is the value of \( y \) when \( x = 0 \). From the first point (0, -2), we can see that the y-intercept \( b = -2 \).

### Summary

- Slope (m): \( 1 \)
- Y-intercept (b): \( -2 \)

The equation of the line can be expressed in slope-intercept form \( y = mx + b \):

\[
y = 1x - 2 \quad \text{or simply} \quad y = x - 2
\]