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katrin [286]
2 years ago
6

Write this down in standard form equation: slope = -1, (2, 5)

Mathematics
1 answer:
kykrilka [37]2 years ago
6 0

Answer:

x+y=7

Step-by-step explanation:

Hi there!

We are given a slope of -1, and the point (2,5)

We want to write an equation of the line in standard form

  • Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero, and a cannot be negative

One way to write the equation of the line in standard form is to first write it in slope-intercept form, and then convert to standard form.

  • Slope intercept form is written as y=mx+b, where m is the slope and b is the y intercept

Since we are already given the slope of the line (-1), we can immediately plug it into the equation y=mx+b

y=-1x+b, or y=-x+b

Now we need to solve for b

As the equation should contain the point (2, 5), it should pass through that point; therefore, it is a solution to the equation, and we can use it to help solve for b

substitute 2 as x and 5 as y:

5=-1(2)+b

Multiply

5=-2+b

add 2 to both sides

7=b

Substitute 7 as b:

y=-x+7

Now we have the equation in slope-intercept form, but remember; we want it in standard form.

Standard form has both x and y on one side, so we can add x to both sides to convert to standard form.

x + y = 7

The equation is written in standard form; a and b (the coefficients in front of x and y) are both not zero, and a is not negative. So we are done.

Hope this helps!

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If we use variables to represent the box contents, we can write ...

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Then the values of x and y are ...

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For positive integer values of the variables, x will always be positive, and y may or may not be negative.

<h3>Smallest sum</h3>

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

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(note that the values of 'b' and 'c' can be swapped with no net effect)

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<em>Additional comment</em>

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

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