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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 answer

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

  1. Calculate the slope \( m \) using the two points given: \( (-3, -1) \) and \( (2, 4) \).

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1 \]

  1. Use one of the points to find the y-intercept \( b \). We will use the point \( (2, 4) \) for this calculation.

Substituting the values into the equation \( y = mx + b \):

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

This simplifies to:

\[ 4 = 2 + b \]

Now, solving for \( b \):

\[ b = 4 - 2 = 2 \]

  1. Write the final equation:

Now that we have the slope \( m = 1 \) and the y-intercept \( b = 2 \), the equation of the line is:

\[ y = 1x + 2 \]

Or simply:

\[ y = x + 2 \]

Thus, the final answer is:

\[ y = x + 2 \]