Use the image to answer the question.

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
y
=
m
x
+
b
form.

Answer 1

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

Step 1: Find the slope \( m \)

The formula to calculate 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 slope formula:

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

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

We can use one of the points and the slope to find the y-intercept. Let's use the point \((2, 4)\) and the slope \( m = 1 \):

The equation of a line can also be written in point-slope form:

\[ y - y_1 = m(x - x_1) \]

Substituting \( m = 1 \), \( x_1 = 2 \), and \( y_1 = 4\):

\[ y - 4 = 1(x - 2) \]

Simplifying this equation:

\[ y - 4 = x - 2 \] \[ y = x + 2 \]

So, the y-intercept \( b = 2 \).

Final Equation:

Putting it all together, the equation of the line is:

\[ y = 1x + 2 \]

or simply:

\[ y = x + 2 \]