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Question

Equations of Linear Functions Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 6 to 6 in one unit increments. The y-axis ranges from negative 4 to 6 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 3 comma negative 1 right parenthesis and left parenthesis 2 comma 4 right parenthesis.

Write the equation of the linear function shown on the graph. Enter your answer in \(y=mx+b\) form.

(1 point)

Answer 1

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

1. Calculate 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 \((-3, -1)\) and \((2, 4)\):

• \((x_1, y_1) = (-3, -1)\)
• \((x_2, y_2) = (2, 4)\)

Substituting these values into the formula:

\[ m = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1 \]

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

2. Use one point to find the y-intercept (b):

The equation is now \(y = 1x + b\) or \(y = x + b\). We'll use one of the points to find \(b\). Let's use the point \((2, 4)\):

\[ 4 = 1(2) + b \]

Calculating:

\[ 4 = 2 + b \]

Subtracting 2 from both sides gives:

\[ b = 4 - 2 = 2 \]

3. Write the final equation:

Now we can write the equation of the line:

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

Therefore, the equation of the linear function is:

\[ \boxed{y = x + 2} \]