Q. 21 Find the intercepts and graph ea... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 1: Q. 21 (page 24)

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$9 x^{2} + 4 y = 36$ .

Short Answer

Expert verified

The intercepts are :

x-intercepts are $(- 2, 0)$ and $(2, 0)$ ,

y-intercept is $(0, 9)$ .

Step by step solution

Given information:

Consider the equation,

$9 x^{2} + 4 y = 36$

To find the x-intercept:

Let $y = 0$ in the equation,

Then, $9 x^{2} + 4 脳 0 = 36$

$9 x^{2} = 36$

$\frac{9 x^{2}}{9} = \frac{36}{9}$ [Divide by 9 on both sides.]

$x^{2} = 4$

$x^{2} - 4 = 4 - 4$ [Add $(- 4)$ on both sides.]

$x^{2} - 4 = 0$

$(x + 2) (x - 2) = 0$ [Factors]

$x + 2 = 0$ or $x - 2 = 0$ [Zero Product Property]

$x = - 2$ or $x = 2$

The equation has two solutions, $- 2 a n d 2 .$

$x - i n t e r c e p t s a r e (- 2, 0) a n d (2, 0) .$

To find the y-intercept:

Let $x = 0$ in the equation,

Then, $9 脳 0 + 4 y = 36$

$4 y = 36$

$\frac{4 y}{4} = \frac{36}{4}$

$y = 9$

$y - i n t e r c e p t i s (0, 9) .$

To draw the graph:

We can draw the graph of the equation $9 x^{2} + 4 y = 36$ by plotting the above intercepts and the points in the table below,

$x$	$y = \frac{36 - 9 x^{2}}{4}$	$(x, y)$
$- 3$	$\frac{- 45}{4}$	$(- 3, \frac{- 45}{4})$
$- 1$	$\frac{27}{4}$	$(- 1, \frac{27}{4})$
$1$	$\frac{27}{4}$	$(1, \frac{27}{4})$
$3$	$\frac{- 45}{4}$	$(3, \frac{- 45}{4})$

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91影视

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$9 x^{2} + 4 y = 36$ .

Short Answer

Step by step solution

Given information:

To find the x-intercept:

To find the y-intercept:

To draw the graph:

One App. One Place for Learning.

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91影视

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.9x2+4y=36.

Short Answer

Step by step solution

Given information:

To find the x-intercept:

To find the y-intercept:

To draw the graph:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Geometry

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.
$9 x^{2} + 4 y = 36$ .