An equation of the line with slope -1 that passes through the point (2,5) is y=-x+7
Correct
Bob, is there anyway you can show work. Sorry forgot to ask
y=mx+b
y=-x+b
5=-2+b
b=7
To obtain the equation of a line with a given slope that passes through a given point, you can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given as:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the coordinates of the given point, and m represents the slope of the line.
In this case, the slope given is -1, and the point given is (2,5). We can substitute these values into the point-slope form to find the equation.
Plugging the values into the point-slope form equation, we get:
y - 5 = -1(x - 2)
Expanding the equation:
y - 5 = -x + 2
Now, simplify the equation by combining like terms:
y = -x + 2 + 5
y = -x + 7
Thus, the equation of the line with a slope of -1 that passes through the point (2,5) is y = -x + 7.