Question

given the table below, write a linear equation that defines the dependent variable in terms of the independent variable. use x for the independent variable and y for the dependent variable.

square footage (x)	total cost (y)
1	106
2	212
3	318

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write the equation of the line described below in slope - intercept form

find the equation of the line that is perpendicular to the line y = 4x - 3 and passes through the point (-10,1).

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,0)$ and $(1,106)$, we have $m=\frac{106 - 0}{1 - 0}=106$.

Step2: Determine the y - intercept

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. When $x = 0$, $y=0$. Substituting into $y=mx + b$, we get $0=106\times0 + b$, so $b = 0$.

Step3: Write the linear equation

Substituting $m = 106$ and $b = 0$ into $y=mx + b$, the linear equation is $y = 106x$.

Answer:

$y = 106x$