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Math  /  Algebra

Question4. Write the equation for the line that represents the relationship shown in the table. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 0 & 8 \\ \hline 3 & 6 \\ \hline 6 & 4 \\ \hline 9 & 2 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The table represents a linear relationship between x x and y y .
2. We need to find the equation of the line in the form y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.

STEP 2

1. Determine the slope m m of the line.
2. Use the slope and one point to find the y-intercept b b .
3. Write the equation of the line.

STEP 3

To find the slope m m , use the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Choose two points from the table, for example, (0,8)(0, 8) and (3,6)(3, 6).
m=6−83−0=−23 m = \frac{6 - 8}{3 - 0} = \frac{-2}{3}

STEP 4

Now, use the slope m=−23 m = -\frac{2}{3} and one of the points, say (0,8)(0, 8), to find the y-intercept b b .
Since the point (0,8)(0, 8) is on the y-axis, the y-coordinate of this point is the y-intercept.
Thus, b=8 b = 8 .

STEP 5

Now that we have both the slope m=−23 m = -\frac{2}{3} and the y-intercept b=8 b = 8 , we can write the equation of the line:
y=−23x+8 y = -\frac{2}{3}x + 8

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