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Which rule describes the relationship between the
x - and
y-coordinates on the following graph?

Which rule describes the relationship between the $x$ - and $y$ -coordinates on the following graph?

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Rational functions: asymptotes and excluded values

Full solution

Q. Which rule describes the relationship between the

x

- and

y

-coordinates on the following graph?

Pick Points: Look at the graph and pick two points that lie on the line. Let's say the points are $(x_1, y_1)$ and $(x_2, y_2)$ .
Calculate Slope: Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . Suppose we picked points $(2, 4)$ and $(4, 8)$ .
Plug in Values: Plug in the values into the slope formula: $m = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2$ .
Write Equation: Write the slope-intercept form of the equation of a line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Find Y-Intercept: Find the y-intercept $b$ by looking where the line crosses the y-axis. Let's say it crosses at $(0, b)$ .
Final Equation: If the line crosses the y-axis at $(0, 0)$ , then $b = 0$ . So the equation of the line is $y = 2x$ .

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