Final answer:
To find the equation of a line with a slope of -1 going through (-2, 5), we use the point-slope form, yielding y - 5 = -1(x + 2), which simplifies to y = -x + 3, the slope-intercept form, where the true y-intercept is 3 and the line moves downward.
Step-by-step explanation:
To write the equation of a line with a slope of -1 that passes through the point (-2, 5), we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, our point is (-2, 5) and our slope, m, is -1. Therefore, our equation becomes y - 5 = -1(x + 2).
To make the equation easier to work with, we can simplify it to y = -x + 3. Now, the equation is in slope-intercept form, which is written as y = mx + b, where m is the slope, and b is the y-intercept. This form is useful for easily identifying both the slope and the y-intercept of the line.
Notice that although the original prompt incorrectly suggested the y-intercept is 50 and the line rises as the x-value increases, the actual y-intercept for this line is 3, and it moves downward on the graph as the x-value increases due to the negative slope.