The line through (-2, 5) with slope -1
To find the equation of a line given a point and its slope, you can use the point-slope form of a linear equation. The formula is:
y - y1 = m(x - x1)
where (x1, y1) is the given point, m is the slope of the line.
In this case, the given point is (-2, 5), and the slope is -1.
Substituting these values into the formula, we get:
y - 5 = -1(x - (-2))
Simplifying further:
y - 5 = -1(x + 2)
Now, expand the brackets:
y - 5 = -x - 2
Rearranging the equation to have y on one side and everything else on the other side:
y = -x - 2 + 5
Simplifying:
y = -x + 3
Therefore, the equation of the line that passes through the point (-2, 5) with a slope of -1 is y = -x + 3.