Graph y=3x

Problem

$y=3x$

Solution

1. Identify the type of equation. The equation $y=3x$ is a linear equation in slope-intercept form $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept.

2. Determine the y-intercept. Since there is no constant term added to $3x$ the y-intercept is $b=0$ This means the line passes through the origin $(0,0)$

3. Determine the slope. The slope is $m=3$ which can be written as the fraction $\frac{3}{1}$ This represents a "rise" of $3$ units for every "run" of $1$ unit to the right.

4. Calculate additional points to plot. Substitute values for $x$ into the equation to find corresponding $y$ values.

$x=1\Rightarrow y=3\left(1\right)=3$

$x=-1\Rightarrow y=3(-1)=-3$

5. Plot the points $(0,0)$ $(1,3)$ and $(-1,-3)$ on a coordinate plane and draw a straight line through them to complete the graph.

Final Answer

$y=3x$

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