Writing Linear Equations in Slope-Intercept Form Practice

Question

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5 of 55 of 5 Items

Question
Use the table to answer the question.

x
y

−3
0
−2
3
−1
6
Write the equation of the line in slope-intercept form.

(1 point)
y=
x+

Answer 1

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) using the points provided in the table.

The points from the table are:

• (-3, 0)
• (-2, 3)
• (-1, 6)

Step 1: Calculate the slope (m)

The slope (m) is calculated using the formula:

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

Let's use the points (-2, 3) and (-3, 0):

• \(x_1 = -3\), \(y_1 = 0\)
• \(x_2 = -2\), \(y_2 = 3\)

Plugging in these values:

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

Step 2: Find the y-intercept (b)

Using one of the points and the slope, we can plug it into the slope-intercept form to find b. Let's use the point (-3, 0):

\[ 0 = 3(-3) + b \]

\[ 0 = -9 + b \quad \Rightarrow \quad b = 9 \]

Step 3: Write the equation

Now we can write the equation of the line in slope-intercept form:

\[ y = 3x + 9 \]

Thus, the final answer is:

y = 3x + 9