Question

write the equation of the line on the graph in slope-intercept form. the line is going down, and the numbers are (0,1) and (1,-4).

Answer 1

are u sure

Answer 2

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given points are (0, 1) and (1, -4):
- \(x_1 = 0\), \(y_1 = 1\)
- \(x_2 = 1\), \(y_2 = -4\)

Substituting the values:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

2. **Find the y-intercept (b)**. We can use one of the points to find b. We'll use (0, 1):
The formula for the line is \(y = mx + b\):
\[
1 = -5(0) + b
\]
Thus, \(b = 1\).

3. **Write the equation** in slope-intercept form:
\[
y = -5x + 1
\]

So, the equation of the line is:
\[
y = -5x + 1
\]

Answer 3

Yes, let's double-check the steps for finding the equation of the line given the points (0, 1) and (1, -4):

1. **Identify the points**:
- Point 1: \((x_1, y_1) = (0, 1)\)
- Point 2: \((x_2, y_2) = (1, -4)\)

2. **Calculate the slope (m)**:
The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the values:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

3. **Find the y-intercept (b)**:
We can use the y-intercept directly from point (0, 1), where \(x = 0\) gives us \(y = b\):
Hence, \(b = 1\).

4. **Write the equation in slope-intercept form**:
With \(m = -5\) and \(b = 1\), the equation is:
\[
y = -5x + 1
\]

Therefore, the equation of the line is indeed:
\[
y = -5x + 1
\]

If there is a specific aspect of the solution that seems unclear or incorrect, please let me know!