Question

Determine the intercepts of the line.

Do not round your answers.
-4x+7y=3−4x+7y=3minus, 4, x, plus, 7, y, equals, 3
xxx-intercept: \Big((left parenthesis
,,comma
\Big))right parenthesis
yyy-intercept: \Big((left parenthesis
,,comma
\Big))right parenthesis

Answer 1

• x-intercept: (-3/4, 0)
• y-intercept: (0, 3/7)

Explanation:

You want the x- and y-intercept coordinates for the line -4x +7y = 3.

X-intercept

The x-intercept is the value of x that corresponds to a y-value of 0. Substituting y=0 into the equation, we have ...

-4x +0 = 3

x = -3/4

The coordinates of the x-intercept point are (-3/4, 0).

Y-intercept

The y-intercept is the value of y that corresponds to an x-value of 0. Substituting x=0 into the equation, we have ...

0 +7y = 3

y = 3/7

The coordinates of the y-intercept point are (0, 3/7).

The intercepts are ...

• x-intercept: (-3/4, 0)
• y-intercept: (0, 3/7)

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Additional comment

We often express the intercept using only the coordinate on the respective axis. The other coordinate is always zero.

The attached graph shows decimal approximations of the intercept points. The value 0.429 corresponds to the decimal value 0.428571...(repeating), or 3/7. Of course -0.75 = -3/4.

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