Math / Algebra

Questionarcepts of the Iraph the ntercept: $\qquad$ itercept:
9. Consider the graph in lem 12 . Which points represent ordered pairs that are solutions of the equation $4 x+3 y=-24$ ? Select all that apply. (3pts) A. the $x$ -intercept of the graph B. the $y$ -intercept of the graph C. the origin D. points that lie close to the line $\square$ E. points that lie on the line

Studdy Solution

STEP 1

1. We are given the equation of a line: $4x + 3y = -24$ .
2. We need to determine which points are solutions to this equation.
3. Solutions to the equation are points that satisfy the equation when substituted for $x$ and $y$ .

STEP 2

1. Find the $x$ -intercept of the line.
2. Find the $y$ -intercept of the line.
3. Determine if the origin is a solution.
4. Analyze points that lie close to the line.
5. Analyze points that lie on the line.

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $4x + 3y = -24$ .
$4x + 3(0) = -24$ $4x = -24$ $x = -6$
The $x$ -intercept is $(-6, 0)$ .

STEP 4

To find the $y$ -intercept, set $x = 0$ in the equation $4x + 3y = -24$ .
$4(0) + 3y = -24$ $3y = -24$ $y = -8$
The $y$ -intercept is $(0, -8)$ .

STEP 5

Check if the origin $(0, 0)$ is a solution by substituting into the equation:
$4(0) + 3(0) = 0 \neq -24$
The origin is not a solution.

STEP 6

Points that lie close to the line are not necessarily solutions unless they satisfy the equation exactly.

STEP 7

Points that lie on the line are solutions because they satisfy the equation $4x + 3y = -24$ .
The points that represent ordered pairs that are solutions of the equation are: - A. the $x$ -intercept of the graph - B. the $y$ -intercept of the graph - E. points that lie on the line

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Studdy Solution

STEP 1

1. We are given the equation of a line: $4x + 3y = -24$ .
2. We need to determine which points are solutions to this equation.
3. Solutions to the equation are points that satisfy the equation when substituted for $x$ and $y$ .

STEP 2

1. Find the $x$ -intercept of the line.
2. Find the $y$ -intercept of the line.
3. Determine if the origin is a solution.
4. Analyze points that lie close to the line.
5. Analyze points that lie on the line.

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $4x + 3y = -24$ .
$4x + 3(0) = -24$ $4x = -24$ $x = -6$
The $x$ -intercept is $(-6, 0)$ .

STEP 4

To find the $y$ -intercept, set $x = 0$ in the equation $4x + 3y = -24$ .
$4(0) + 3y = -24$ $3y = -24$ $y = -8$
The $y$ -intercept is $(0, -8)$ .

STEP 5

Check if the origin $(0, 0)$ is a solution by substituting into the equation:
$4(0) + 3(0) = 0 \neq -24$
The origin is not a solution.

STEP 6

Points that lie close to the line are not necessarily solutions unless they satisfy the equation exactly.

STEP 7

Points that lie on the line are solutions because they satisfy the equation $4x + 3y = -24$ .
The points that represent ordered pairs that are solutions of the equation are: - A. the $x$ -intercept of the graph - B. the $y$ -intercept of the graph - E. points that lie on the line

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Studdy Solution

STEP 1

1. We are given the equation of a line: 4x+3y=−24 4x + 3y = -24 4x+3y=−24.2. We need to determine which points are solutions to this equation.3. Solutions to the equation are points that satisfy the equation when substituted for x x x and y y y.

STEP 2

1. Find the x x x-intercept of the line.2. Find the y y y-intercept of the line.3. Determine if the origin is a solution.4. Analyze points that lie close to the line.5. Analyze points that lie on the line.

STEP 3

To find the x x x-intercept, set y=0 y = 0 y=0 in the equation 4x+3y=−24 4x + 3y = -24 4x+3y=−24.4x+3(0)=−24 4x + 3(0) = -24 4x+3(0)=−24 4x=−24 4x = -24 4x=−24 x=−6 x = -6 x=−6The x x x-intercept is (−6,0) (-6, 0) (−6,0).

STEP 4

To find the y y y-intercept, set x=0 x = 0 x=0 in the equation 4x+3y=−24 4x + 3y = -24 4x+3y=−24.4(0)+3y=−24 4(0) + 3y = -24 4(0)+3y=−24 3y=−24 3y = -24 3y=−24 y=−8 y = -8 y=−8The y y y-intercept is (0,−8) (0, -8) (0,−8).

STEP 5

Check if the origin (0,0)(0, 0)(0,0) is a solution by substituting into the equation:4(0)+3(0)=0≠−24 4(0) + 3(0) = 0 \neq -24 4(0)+3(0)=0=−24The origin is not a solution.

STEP 6

Points that lie close to the line are not necessarily solutions unless they satisfy the equation exactly.

STEP 7

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1. We are given the equation of a line: $4x + 3y = -24$ .
2. We need to determine which points are solutions to this equation.
3. Solutions to the equation are points that satisfy the equation when substituted for $x$ and $y$ .

1. Find the $x$ -intercept of the line.
2. Find the $y$ -intercept of the line.
3. Determine if the origin is a solution.
4. Analyze points that lie close to the line.
5. Analyze points that lie on the line.

To find the $x$ -intercept, set $y = 0$ in the equation $4x + 3y = -24$ .
$4x + 3(0) = -24$ $4x = -24$ $x = -6$
The $x$ -intercept is $(-6, 0)$ .

To find the $y$ -intercept, set $x = 0$ in the equation $4x + 3y = -24$ .
$4(0) + 3y = -24$ $3y = -24$ $y = -8$
The $y$ -intercept is $(0, -8)$ .

Check if the origin $(0, 0)$ is a solution by substituting into the equation:
$4(0) + 3(0) = 0 \neq -24$
The origin is not a solution.