Writing Linear Equations in Slope-Intercept Form Practice

Question

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Question
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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: \[ y = 2x - 1 \]