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Math  /  Algebra

QuestionFind the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}
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Studdy Solution

STEP 1

1. The relationship between xx and yy is linear.
2. The slope-intercept form of a linear equation is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
3. We have sufficient data to determine both the slope and the y-intercept from the table.

STEP 2

1. Calculate the slope mm using two points from the table.
2. Use the slope and one point to solve for the y-intercept bb.
3. Write the equation in slope-intercept form.

STEP 3

Select two points from the table to calculate the slope mm. Let's use the points (1,−9)(1, -9) and (2,−13)(2, -13).
The formula for the slope mm is:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the values:
m=−13−(−9)2−1=−13+91=−41=−4 m = \frac{-13 - (-9)}{2 - 1} = \frac{-13 + 9}{1} = \frac{-4}{1} = -4

STEP 4

Use the slope m=−4m = -4 and one of the points, say (1,−9)(1, -9), to find the y-intercept bb.
Substitute into the slope-intercept form y=mx+by = mx + b:
−9=−4(1)+b -9 = -4(1) + b
Solve for bb:
−9=−4+b -9 = -4 + b
b=−9+4 b = -9 + 4
b=−5 b = -5

STEP 5

Write the equation of the line in slope-intercept form using the calculated slope and y-intercept:
y=−4x−5 y = -4x - 5
The equation of the linear function is:
y=−4x−5 \boxed{y = -4x - 5}

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