Math / Geometry

QuestionFind the $x$ -intercept and the $y$ -intercept. Then graph the equation. $x+8=0$ A. The x-intercept is $(-8,0)$ . (Type an ordered pair.) B. The equation has no x-intercept.
Find the $y$ -intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$ -intercept is $\square$ . ITuno an nrdarad nair)

Studdy Solution

STEP 1

1. The equation provided is $x + 8 = 0$ .
2. The $x$ -intercept occurs where the graph intersects the $x$ -axis, i.e., where $y = 0$ .
3. The $y$ -intercept occurs where the graph intersects the $y$ -axis, i.e., where $x = 0$ .
4. The goal is to find both the $x$ -intercept and the $y$ -intercept of the given equation.

STEP 2

1. Determine the $x$ -intercept of the equation.
2. Determine the $y$ -intercept of the equation.
3. Draw the graph of the equation.

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $x + 8 = 0$ .
$x + 8 = 0$

STEP 4

Solve for $x$ .
$x = -8$

STEP 5

Thus, the $x$ -intercept is $(-8, 0)$ .

STEP 6

To find the $y$ -intercept, set $x = 0$ in the equation $x + 8 = 0$ .
$0 + 8 = 0$

STEP 7

Check the equation:
$8 = 0$

STEP 8

Since $8 \neq 0$ , there is no solution for $y$ when $x = 0$ . Hence, there is no $y$ -intercept.

STEP 9

To graph the equation $x + 8 = 0$ , recognize that it represents a vertical line passing through $x = -8$ .
1. Draw a vertical line at $x = -8$ .
2. Note that this line will not intersect the $y$ -axis.
Solution: - The $x$ -intercept is $(-8, 0)$ . - The equation has no $y$ -intercept.

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Studdy Solution

STEP 1

STEP 2

1. Determine the $x$ -intercept of the equation.
2. Determine the $y$ -intercept of the equation.
3. Draw the graph of the equation.

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $x + 8 = 0$ .
$x + 8 = 0$

STEP 4

Solve for $x$ .
$x = -8$

STEP 5

Thus, the $x$ -intercept is $(-8, 0)$ .

STEP 6

To find the $y$ -intercept, set $x = 0$ in the equation $x + 8 = 0$ .
$0 + 8 = 0$

STEP 7

Check the equation:
$8 = 0$

STEP 8

Since $8 \neq 0$ , there is no solution for $y$ when $x = 0$ . Hence, there is no $y$ -intercept.

STEP 9

To graph the equation $x + 8 = 0$ , recognize that it represents a vertical line passing through $x = -8$ .
1. Draw a vertical line at $x = -8$ .
2. Note that this line will not intersect the $y$ -axis.
Solution: - The $x$ -intercept is $(-8, 0)$ . - The equation has no $y$ -intercept.

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Studdy Solution

STEP 1

STEP 2

1. Determine the xxx-intercept of the equation.2. Determine the yyy-intercept of the equation.3. Draw the graph of the equation.

STEP 3

To find the xxx-intercept, set y=0y = 0y=0 in the equation x+8=0x + 8 = 0x+8=0.x+8=0 x + 8 = 0 x+8=0

STEP 4

Solve for xxx.x=−8 x = -8 x=−8

STEP 5

Thus, the xxx-intercept is (−8,0)(-8, 0)(−8,0).

STEP 6

To find the yyy-intercept, set x=0x = 0x=0 in the equation x+8=0x + 8 = 0x+8=0.0+8=0 0 + 8 = 0 0+8=0

STEP 7

Check the equation:8=0 8 = 0 8=0

STEP 8

Since 8≠08 \neq 08=0, there is no solution for yyy when x=0x = 0x=0. Hence, there is no yyy-intercept.

STEP 9

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1. Determine the $x$ -intercept of the equation.
2. Determine the $y$ -intercept of the equation.
3. Draw the graph of the equation.

To find the $x$ -intercept, set $y = 0$ in the equation $x + 8 = 0$ .
$x + 8 = 0$

Solve for $x$ .
$x = -8$

Thus, the $x$ -intercept is $(-8, 0)$ .

To find the $y$ -intercept, set $x = 0$ in the equation $x + 8 = 0$ .
$0 + 8 = 0$

Check the equation:
$8 = 0$

Since $8 \neq 0$ , there is no solution for $y$ when $x = 0$ . Hence, there is no $y$ -intercept.