Question

Writing Linear Equations in Slope-Intercept Form Practice
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Question
Use the image to answer the question.

A coordinate plane of 4 quadrants shows x and y axes ranging from negative 3 to 3 in increments of 1. A line with arrows at each end intercepts two plotted points, A and B. Point A is plotted at left parenthesis 0 comma negative 1 right parenthesis. Point B is plotted at left parenthesis 1 comma 1 right parenthesis. The coordinates are not labeled.

Write the equation of the line in slope-intercept form.

(1 point)
y=
x+
(
)

Answer 1

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

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

The slope \(m\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points A (0, -1) and B (1, 1):
- \(y_1 = -1\), \(x_1 = 0\)
- \(y_2 = 1\), \(x_2 = 1\)

Now plug the values into the formula:
\[
m = \frac{1 - (-1)}{1 - 0} = \frac{1 + 1}{1 - 0} = \frac{2}{1} = 2
\]

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

Since point A is at (0, -1), this means that when \(x = 0\), \(y = -1\). Thus, the y-intercept \(b = -1\).

### Step 3: Write the equation

Now we have:
- slope \(m = 2\)
- y-intercept \(b = -1\)

Putting it all together, the equation in slope-intercept form is:
\[
y = 2x - 1
\]

### Final Answer

Therefore, the answer is:
\[
y = 2x - 1
\]