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, $9 x^{2} + 4 \times 0 = 36$

$9 x^{2} = 36$

$\frac{9 x^{2}}{9} = \frac{36}{9}$ [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, $9 \times 0 + 4 y = 36$

$4 y = 36$

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

$y = 9$

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

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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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:

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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

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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