Q. What is the y-intercept of \(f(x) = 3x + 2\)?

Q: What is the y-intercept of f(x)=3x+2?

Plug in x=0: f(0)=2. The y-intercept is the point (0,2).

Q: How do I find the x-intercept of f(x)=3x+2?

Set f(x)=0: 3x + 2 = 0, so x = -\frac{2}{3}. The x-intercept is \left(-\frac{2}{3}, 0\right).

Q: What is the slope of f(x)=3x+2?

In slope–intercept form y=mx+b, the slope m is 3.

Q: Why is the y-intercept the constant term in y=mx+b?

Because when x=0 the term mx vanishes, leaving y=b. Thus b is the y-coordinate where the line crosses the y-axis.

Q: How do I quickly graph y=3x+2?

Plot the y-intercept (0,2), then use the slope rise/run 3/1: from (0,2) go up 3 and right 1 to get another point, draw the line through them.

Q: How would the graph shift if the equation were y=3x+5?

How would the graph shift if the equation were y=3x+5?

Q: How do I write y=3x+2 in standard form?

Rearranged: 3x-y=-2 (or equivalently 3x-y+2=0), which is the standard linear form Ax+By=C.

Q: Given slope 3 and y-intercept (0,2), how to write the equation?

Use slope–intercept: y=mx+b with m=3 and b=2, so the equation is y=3x+2.

Answer

Evaluate at x = 0: (f(0) = 3 \cdot 0 + 2 = 2).
Y-intercept: ((0,2))

Detailed Explanation

Solution

Definition and what to do: The y-intercept is the point where the graph crosses the y-axis. Every point on the y-axis has x = 0, so evaluate the function at x = 0.
Substitute x = 0 into the function \(f(x) = 3x + 2\). Compute:
\[
f(0) = 3(0) + 2
\]
Simplify the arithmetic step by step:
\[
f(0) = 0 + 2
\]
\[
f(0) = 2
\]
So the y-coordinate of the intercept is 2.
State the y-intercept as a point and as a y-value: the graph crosses the y-axis at the point \((0,2)\), and the y-intercept (the y-value) is 2.
Alternatively, noting that the equation is in slope-intercept form \(y = mx + b\), the intercept \(b\) equals 2.

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FAQs

What is the y-intercept of \(f(x)=3x+2\)?

Plug in \(x=0\): \(f(0)=2\). The y-intercept is the point \((0,2)\).

How do I find the x-intercept of \(f(x)=3x+2\)?

Set \(f(x)=0\): \(3x + 2 = 0\), so \(x = -\frac{2}{3}\). The x-intercept is \(\left(-\frac{2}{3}, 0\right)\).

What is the slope of \(f(x)=3x+2\)?

In slope–intercept form \(y=mx+b\), the slope \(m\) is \(3\).

Why is the y-intercept the constant term in \(y=mx+b\)?

Because when \(x=0\) the term \(mx\) vanishes, leaving \(y=b\). Thus \(b\) is the y-coordinate where the line crosses the y-axis.

How do I quickly graph \(y=3x+2\)?

Plot the y-intercept \((0,2)\), then use the slope rise/run \(3/1\): from \((0,2)\) go up 3 and right 1 to get another point, draw the line through them.

How would the graph shift if the equation were \(y=3x+5\)?

How do I write \(y=3x+2\) in standard form?

Rearranged: \(3x-y=-2\) (or equivalently \(3x-y+2=0\)), which is the standard linear form \(Ax+By=C\).

Given slope \(3\) and y-intercept \((0,2)\), how to write the equation?

Use slope–intercept: \(y=mx+b\) with \(m=3\) and \(b=2\), so the equation is \(y=3x+2\).

Find the y-intercept of f(x) = 3x+2.
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