Questions: Solve for y - STAAR Problems Google Form Due: Fri Sep 13, 2024 11:59pm 50 The table represents some points on the graph of a linear function. x y -20 -268 -14 -196 -8 -124 -1 -40 Which equation represents the same relationship? F y+268=(1/12)(x+20) G y+20=(1/12)(x+268) H y+268=12(x+20) ] y+20=12(x+268)

Solution Steps

To find the equation that represents the relationship given by the table, we need to determine the slope and y-intercept of the linear function. We can use the formula for the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ using any two points from the table. Once we have the slope, we can use the point-slope form of a linear equation $y - y_1 = m(x - x_1)$ to find the equation. Finally, we compare the derived equation with the given options to find the correct one.

To find the slope $m$ of the linear function, we use the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Using the points $(-20, -268)$ and $(-14, -196)$:

$$m = \frac{-196 - (-268)}{-14 - (-20)} = \frac{72}{6} = 12.0$$

Using the slope $m = 12.0$ and the point $(-20, -268)$, we can find the y-intercept $b$ using the point-slope form of the equation:

$$y - y_1 = m(x - x_1)$$

Substituting the values:

$$-268 = 12.0(-20) + b$$

Solving for $b$:

$$-268 = -240 + b \implies b = -28.0$$

The equation of the line in slope-intercept form is:

$$y = mx + b$$

Substituting the values of $m$ and $b$:

$$y = 12.0x - 28.0$$

We compare the derived equation $y = 12.0x - 28.0$ with the given options:

• Option F: $y + 268 = \frac{1}{12}(x + 20)$
• Option G: $y + 20 = \frac{1}{12}(x + 268)$
• Option H: $y + 268 = 12(x + 20)$
• Option I: $y + 20 = 12(x + 268)$

Rewriting Option H:

$$y + 268 = 12(x + 20) \implies y = 12x + 240 - 268 \implies y = 12x - 28$$

This matches the derived equation.

Final Answer