Math / Algebra

QuestionFor which values of $A, B$ , and $C$ will $A x+B y=C$ be a horizontal line through the point $(-4,2) ?$ $A=\square, B=\square, C=\square$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $A$ , $B$ , and $C$ that make the equation $A x + B y = C$ represent a horizontal line passing through the point $(-4, 2)$ . Watch out! Horizontal lines have a slope of zero, so be careful not to mix them up with vertical lines!

STEP 2

1. Analyze the horizontal line
2. Find the equation
3. Determine the values

STEP 3

Alright, so we're dealing with a horizontal line.
What does that even mean?
It means that the y-value stays the same, no matter what the x-value is!
Think of it like the horizon – it goes on forever sideways, but it doesn't go up or down.

STEP 4

Since the y-value is always the same, we can write the equation of a horizontal line as $y = k$ , where $k$ is some constant value.

STEP 5

We know our horizontal line goes through the point $(-4, 2)$ .
This tells us that the y-value is always 2, no matter what x is.
So, our equation is $y = 2$ .

STEP 6

Now, we need to make this equation look like $A x + B y = C$ .
We can do this by adding zero to both sides of the equation.
We'll add $0 \cdot x$ to the left side and $0$ to the right side.
This gives us $0 \cdot x + y = 2$ .

STEP 7

Comparing $0 \cdot x + y = 2$ to $A x + B y = C$ , we can see that $A = 0$ , $B = 1$ , and $C = 2$ .
Boom! We found our values!

STEP 8

$A = 0, \quad B = 1, \quad C = 2$

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QuestionFor which values of $A, B$ , and $C$ will $A x+B y=C$ be a horizontal line through the point $(-4,2) ?$ $A=\square, B=\square, C=\square$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $A$ , $B$ , and $C$ that make the equation $A x + B y = C$ represent a horizontal line passing through the point $(-4, 2)$ . Watch out! Horizontal lines have a slope of zero, so be careful not to mix them up with vertical lines!

STEP 2

1. Analyze the horizontal line
2. Find the equation
3. Determine the values

STEP 3

Alright, so we're dealing with a horizontal line.
What does that even mean?
It means that the y-value stays the same, no matter what the x-value is!
Think of it like the horizon – it goes on forever sideways, but it doesn't go up or down.

STEP 4

Since the y-value is always the same, we can write the equation of a horizontal line as $y = k$ , where $k$ is some constant value.

STEP 5

We know our horizontal line goes through the point $(-4, 2)$ .
This tells us that the y-value is always 2, no matter what x is.
So, our equation is $y = 2$ .

STEP 6

Now, we need to make this equation look like $A x + B y = C$ .
We can do this by adding zero to both sides of the equation.
We'll add $0 \cdot x$ to the left side and $0$ to the right side.
This gives us $0 \cdot x + y = 2$ .

STEP 7

Comparing $0 \cdot x + y = 2$ to $A x + B y = C$ , we can see that $A = 0$ , $B = 1$ , and $C = 2$ .
Boom! We found our values!

STEP 8

$A = 0, \quad B = 1, \quad C = 2$

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QuestionFor which values of A,BA, BA,B, and CCC will Ax+By=CA x+B y=CAx+By=C be a horizontal line through the point (−4,2)?(-4,2) ?(−4,2)? A=□,B=□,C=□A=\square, B=\square, C=\squareA=□,B=□,C=□

Studdy Solution

STEP 1

STEP 2

1. Analyze the horizontal line2. Find the equation3. Determine the values

STEP 3

Alright, so we're dealing with a **horizontal line**.What does that even mean?It means that the *y*-value stays the **same**, no matter what the *x*-value is!Think of it like the horizon – it goes on forever sideways, but it doesn't go up or down.

STEP 4

Since the *y*-value is always the same, we can write the equation of a horizontal line as y=ky = ky=k, where kkk is some **constant value**.

STEP 5

We know our horizontal line goes through the point (−4,2)(-4, 2)(−4,2).This tells us that the *y*-value is always **2**, no matter what *x* is.So, our equation is y=2y = 2y=2.

STEP 6

Now, we need to make this equation look like Ax+By=CA x + B y = CAx+By=C.We can do this by adding zero to both sides of the equation.We'll add 0⋅x0 \cdot x0⋅x to the left side and 000 to the right side.This gives us 0⋅x+y=20 \cdot x + y = 20⋅x+y=2.

STEP 7

Comparing 0⋅x+y=20 \cdot x + y = 20⋅x+y=2 to Ax+By=CA x + B y = CAx+By=C, we can see that A=0A = 0A=0, B=1B = 1B=1, and C=2C = 2C=2.Boom! We found our values!

STEP 8

A=0,B=1,C=2A = 0, \quad B = 1, \quad C = 2A=0,B=1,C=2

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Studdy solves anything!

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QuestionFor which values of $A, B$ , and $C$ will $A x+B y=C$ be a horizontal line through the point $(-4,2) ?$ $A=\square, B=\square, C=\square$

1. Analyze the horizontal line
2. Find the equation
3. Determine the values

Alright, so we're dealing with a horizontal line.
What does that even mean?
It means that the y-value stays the same, no matter what the x-value is!
Think of it like the horizon – it goes on forever sideways, but it doesn't go up or down.

Since the y-value is always the same, we can write the equation of a horizontal line as $y = k$ , where $k$ is some constant value.

We know our horizontal line goes through the point $(-4, 2)$ .
This tells us that the y-value is always 2, no matter what x is.
So, our equation is $y = 2$ .

Now, we need to make this equation look like $A x + B y = C$ .
We can do this by adding zero to both sides of the equation.
We'll add $0 \cdot x$ to the left side and $0$ to the right side.
This gives us $0 \cdot x + y = 2$ .

Comparing $0 \cdot x + y = 2$ to $A x + B y = C$ , we can see that $A = 0$ , $B = 1$ , and $C = 2$ .
Boom! We found our values!

$A = 0, \quad B = 1, \quad C = 2$