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How do you find the x and y intercepts for $f (x) = - 3 x - 2$ $f(x) = -3x-2$ ?

1 Answer

Aug 11, 2016

y-intercept: $- 2$ $-2$

x-intercept: $- \frac{2}{3}$ $-2/3$

Explanation:

Note that $f (x)$ $f(x)$ is equivalent to $y$ $y$ .

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The y-intercept is the value on the Y-axis where the function crosses the Y-axis. Since the Y-axis is the collection of points where $x = 0$ $x=0$ , it follows that the y-intercept is the value of the function when $x = 0$ $x=0$ .

Evaluating $f (x) = - 3 x - 2$ $f(x)=-3x-2$ when $x = 0$ $x=0$ :
$XXX f (0) = - 3 (0) - 2 = - 2$ $color(white)("XXX")f(0)=-3(0)-2=-2$
So the y-intercept is at $(- 2)$ $(-2)$

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Similarly, the x-intercept is the value of $x$ $x$ when $y = 0$ $y=0$ (or equivalently when $f (x) = 0$ $f(x)=0$

Evaluating $f (x) = - 3 x - 2$ $f(x)=-3x-2$ when $f (x) = 0$ $f(x)=0$
$XXX 0 = - 3 x - 2$ $color(white)("XXX")0=-3x-2$

$XXX \to - 3 x = 2$ $color(white)("XXX")rarr -3x=2$

$XXX \to x = - \frac{2}{3}$ $color(white)("XXX")rarr x=-2/3$
So the x-intercept is at $(- \frac{2}{3})$ $(-2/3)$

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