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

Sagot :

amysun2025

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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