Question

How do you put the point (0,9) and a slope of 5/4 in standard form?

Answer 1

-5x + 4y = 36

Step-by-step explanation:

The general equation of the standard form of a line is given by:

Ax + By = C, where:

• A, B, and C are constants.

Since we're given a point on the line and the slope, we can start with the point-slope form, whose general equation is given by:

y - y1 = m(x - x1), where:

• (x1, y1) are any point on the line,
• and m is the slope.

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Thus, we first need to substitute (0, 9) for (x1, y1) and 5/4 for m and simplify:

y - 9 = 5/4(x - 0)

y - 9 = (5/4 * x) + (5/4 * -0)

y - 9 = 5/4x + 0

Now, we add 9 to both sides:

(y - 9 = 5/4x + 0) + 9

y = 5/4x + 9

Next, we subtract 5/4x from both sides to put the equation in standard form:

(y = 5/4x + 9) - 5/4x

-5/4x + y = 9

Finally (for the sake of presentation), we can clear the fraction by multiplying both sides by 4:

(-5/4x + y = 9) * 4

-5x + 4y = 36

Therefore, -5x + 4y = 36 is the equation of the line in standard form that passes through the point (0, 9) and has a slope of 5/4.

Answer 2

To put the point (0,9) with a slope of 5/4 into standard form, use the point-slope form and then rearrange the equation by eliminating the fraction and moving terms to get -5x + 4y = 36, which is the standard form Ax + By = C.

Step-by-step explanation:

To convert the point (0,9) with a slope of 5/4 into standard form, we first utilize the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, m = 5/4, and our point is (0,9).

Starting with point-slope form:

y - 9 = 5/4(x - 0)

This simplifies to:

y - 9 = 5/4x

To get the standard form, we want to eliminate the fraction by multiplying all terms by the denominator, 4, and then rearrange the equation to Ax + By = C:

4(y - 9) = 4(5/4x) ⇒ 4y - 36 = 5x

Rearranging gives us:

-5x + 4y = 36

Now we have the standard form, which is Ax + By = C where A, B, and C are integers.