Math / Algebra

QuestionFind the $x$ - and $y$ -intercepts of the graph of $3 x-4 y=27$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2 x-intercept: $\square$ y-intercept: $\square$

Studdy Solution

STEP 1

1. The equation $3x - 4y = 27$ is a linear equation in two variables.
2. The $x$ -intercept is the point where the graph crosses the $x$ -axis, which means $y = 0$ .
3. The $y$ -intercept is the point where the graph crosses the $y$ -axis, which means $x = 0$ .

STEP 2

1. Find the $x$ -intercept by setting $y = 0$ and solving for $x$ .
2. Find the $y$ -intercept by setting $x = 0$ and solving for $y$ .

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $3x - 4y = 27$ :
$3x - 4(0) = 27$
Simplify the equation:
$3x = 27$

STEP 4

Solve for $x$ by dividing both sides by 3:
$x = \frac{27}{3}$
$x = 9$
Thus, the $x$ -intercept is $9$ .

STEP 5

To find the $y$ -intercept, set $x = 0$ in the equation $3x - 4y = 27$ :
$3(0) - 4y = 27$
Simplify the equation:
$-4y = 27$

STEP 6

Solve for $y$ by dividing both sides by $-4$ :
$y = \frac{27}{-4}$
$y = -\frac{27}{4}$
Thus, the $y$ -intercept is $-\frac{27}{4}$ .
Solution: - $x$ -intercept: $9$ - $y$ -intercept: $-\frac{27}{4}$

Was this helpful?

QuestionFind the $x$ - and $y$ -intercepts of the graph of $3 x-4 y=27$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2 x-intercept: $\square$ y-intercept: $\square$

Studdy Solution

STEP 1

1. The equation $3x - 4y = 27$ is a linear equation in two variables.
2. The $x$ -intercept is the point where the graph crosses the $x$ -axis, which means $y = 0$ .
3. The $y$ -intercept is the point where the graph crosses the $y$ -axis, which means $x = 0$ .

STEP 2

1. Find the $x$ -intercept by setting $y = 0$ and solving for $x$ .
2. Find the $y$ -intercept by setting $x = 0$ and solving for $y$ .

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $3x - 4y = 27$ :
$3x - 4(0) = 27$
Simplify the equation:
$3x = 27$

STEP 4

Solve for $x$ by dividing both sides by 3:
$x = \frac{27}{3}$
$x = 9$
Thus, the $x$ -intercept is $9$ .

STEP 5

To find the $y$ -intercept, set $x = 0$ in the equation $3x - 4y = 27$ :
$3(0) - 4y = 27$
Simplify the equation:
$-4y = 27$

STEP 6

Solve for $y$ by dividing both sides by $-4$ :
$y = \frac{27}{-4}$
$y = -\frac{27}{4}$
Thus, the $y$ -intercept is $-\frac{27}{4}$ .
Solution: - $x$ -intercept: $9$ - $y$ -intercept: $-\frac{27}{4}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the xxx - and yyy-intercepts of the graph of 3x−4y=273 x-4 y=273x−4y=27. State each answer as an integer or an improper fraction in simplest form.Answer Attempt 1 out of 2 x-intercept: □\square□ y-intercept: □\square□

Studdy Solution

STEP 1

1. The equation 3x−4y=273x - 4y = 273x−4y=27 is a linear equation in two variables.2. The xxx-intercept is the point where the graph crosses the xxx-axis, which means y=0y = 0y=0.3. The yyy-intercept is the point where the graph crosses the yyy-axis, which means x=0x = 0x=0.

STEP 2

1. Find the xxx-intercept by setting y=0y = 0y=0 and solving for xxx.2. Find the yyy-intercept by setting x=0x = 0x=0 and solving for yyy.

STEP 3

To find the xxx-intercept, set y=0y = 0y=0 in the equation 3x−4y=273x - 4y = 273x−4y=27:3x−4(0)=27 3x - 4(0) = 27 3x−4(0)=27Simplify the equation:3x=27 3x = 27 3x=27

STEP 4

Solve for xxx by dividing both sides by 3:x=273 x = \frac{27}{3} x=327​x=9 x = 9 x=9Thus, the xxx-intercept is 999.

STEP 5

To find the yyy-intercept, set x=0x = 0x=0 in the equation 3x−4y=273x - 4y = 273x−4y=27:3(0)−4y=27 3(0) - 4y = 27 3(0)−4y=27Simplify the equation:−4y=27 -4y = 27 −4y=27

STEP 6

Solve for yyy by dividing both sides by −4-4−4:y=27−4 y = \frac{27}{-4} y=−427​y=−274 y = -\frac{27}{4} y=−427​Thus, the yyy-intercept is −274-\frac{27}{4}−427​. Solution: - xxx-intercept: 999 - yyy-intercept: −274-\frac{27}{4}−427​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the $x$ - and $y$ -intercepts of the graph of $3 x-4 y=27$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2 x-intercept: $\square$ y-intercept: $\square$

1. The equation $3x - 4y = 27$ is a linear equation in two variables.
2. The $x$ -intercept is the point where the graph crosses the $x$ -axis, which means $y = 0$ .
3. The $y$ -intercept is the point where the graph crosses the $y$ -axis, which means $x = 0$ .

1. Find the $x$ -intercept by setting $y = 0$ and solving for $x$ .
2. Find the $y$ -intercept by setting $x = 0$ and solving for $y$ .

To find the $x$ -intercept, set $y = 0$ in the equation $3x - 4y = 27$ :
$3x - 4(0) = 27$
Simplify the equation:
$3x = 27$

Solve for $x$ by dividing both sides by 3:
$x = \frac{27}{3}$
$x = 9$
Thus, the $x$ -intercept is $9$ .

To find the $y$ -intercept, set $x = 0$ in the equation $3x - 4y = 27$ :
$3(0) - 4y = 27$
Simplify the equation:
$-4y = 27$

Solve for $y$ by dividing both sides by $-4$ :
$y = \frac{27}{-4}$
$y = -\frac{27}{4}$
Thus, the $y$ -intercept is $-\frac{27}{4}$ .
Solution: - $x$ -intercept: $9$ - $y$ -intercept: $-\frac{27}{4}$