4 quarts equals how many cups?

Find an equation of the line in the form ax+by=c whose x-intercept is 12 and y-intercept is 4, where a, b, and c are integer

Lostsunrise [7]

Answer:

The equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form $ax+by=c$ where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as $(x,0)$

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as $(0,y)$ .

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

So, slope of the line can b given as:

$m=\frac{4-0}{0-12}$

$m=\frac{4}{-12}$

$m=-\frac{1}{3}$

The slope intercept form of the equation of he line is given as:

$y=mx+b$

where $m$ represents slope of the line and $b$ represents the y-intercept.

So, the equation of the line can be given as:

$y=-\frac{1}{3}x+4$

Multiplying each term by 3 to remove fraction.

$3y=3.-\frac{1}{3}x+4(3)$

$3y=-x+12$

Adding $x$ both sides.

$3y+x=-x+x+12$

$3y+x=12$

Thus, the equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

8 0

3 years ago

ILL GIVE A BRAINLIST :>

sattari [20]

Answer:

B) The exponential function will eventually exceed the linear function.

3 0

4 years ago

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Create and solve a system of equations for the following scenario: Luke and Leia are selling hot dogs and hamburgers at a minor

mixas84 [53]

So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.

5 0

4 years ago

Solve each equation for the bold variable

Phantasy [73]

Answer:

y = 3 - 2x

Step-by-step explanation:

The goal is to isolate the y variable

In order to have y by itself (on one side of the equation or equal sign), we must move the other numbers and variables to the other side.

Since 2x is on the same side as y, we have to subtract it from both sides. Subtracting it cancels out the original 2x and leaves the equation to look like this:

y = 3 - 2x

Now the y is isolated

Another example:

-5x + y = 15

To isolate the y, we must cancel out the -5x. Add 5x to both sides. It will cancel out the -5x and bring it to the right side of the equation, resulting in:

y = 15 + 5x

4 0

3 years ago

Kayla can bake 15 muffins in 2.5 hours. At this rate, how many can she bake in 8 hours?

jenyasd209 [6]

She can bake 48 in 8 hours

6 0

3 years ago

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