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!
