Question

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)
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Answer 1

To find the equation of the linear function, we can use the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

First, let's find the slope, which is the change in y divided by the change in x.
The change in y is 4 - (-1) = 5
The change in x is 2 - (-3) = 5

So, the slope, m, is 5/5 = 1.

Now, let's find the y-intercept, b, which is the y-coordinate when x = 0.
Using the first point, (-3, -1), we can substitute these values into the equation and solve for b:
-1 = 1*(-3) + b
-1 = -3 + b
b = 2

So, the equation of the linear function shown on the graph is y = x + 2.