What is the y-intercept of the graph of the equation y=2x+6?

Understand the Problem

The question is asking for the y-intercept of the linear equation y=2x+6 and how to graph it. The y-intercept is the point where the graph crosses the y-axis, which occurs when x=0.

Answer

The y-intercept is at the point $(0, 6)$.

Steps to Solve

Finding the y-intercept

To find the y-intercept for the equation $y = 2x + 6$, substitute $x = 0$ into the equation.

$$ y = 2(0) + 6 $$

Calculating the value

After substituting, simplify the equation:

$$ y = 0 + 6 $$

So, the y-intercept is $y = 6$.

Identifying the coordinates of the y-intercept

The coordinates of the y-intercept are given by the point where $x = 0$. Therefore, the y-intercept is at the point:

$$ (0, 6) $$

Graphing the linear equation

To graph the equation $y = 2x + 6$, start by plotting the y-intercept $(0, 6)$ on the graph. Next, use the slope, which is $2$. This means that for every 1 unit you move to the right (increase in $x$), you move up 2 units (increase in $y$).

Plotting another point using slope

Starting from the point $(0, 6)$, if you move right 1 unit to $x = 1$, you will then move up 2 units to:

$$ (1, 8) $$

Now you can plot the second point $(1, 8)$ as well.

Drawing the line

Finally, draw a straight line through the points $(0, 6)$ and $(1, 8)$ to complete the graph of the equation.

The y-intercept of the equation $y = 2x + 6$ is at the point $(0, 6)$.

More Information

The y-intercept is important in graphing linear equations as it helps establish a starting point on the graph. The slope indicates the direction and steepness of the line. In this case, a slope of 2 means the line rises steeply.

Tips

Forgetting to substitute $x = 0$ when finding the y-intercept.
Miscalculating the slope when trying to graph the line.
Plotting points incorrectly on the graph by misunderstanding the rise/run concept.

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