What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line #x + y = 13#?

Question

Sadie Adams · Accepted Answer

#color(magenta)(y = -1 * x -1 " is the slope-intercept form of the equation"#

Given line ; # x + y = 13#

#y = -1 * x + 13#

#:. "Slope " = m = -1#

Equation of the parallel line passing through "#(-8,7)# is

#y - y_1 = m * (x - x_1)#

#y - 7 = -1 * (x + 8)#

#color(magenta)(y = -1 * x -1 " is the slope-intercept form of the equation"#

graph{-x -1 [-10, 10, -5, 5]}

Noah Atkinson · Answer

undefined The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of the line parallel to x + y = 13, we first need to determine the slope of the given line. Rearranging the equation x + y = 13 into slope-intercept form, we get y = -x + 13.

Since parallel lines have the same slope, the slope of the line we're looking for will also be -1. Using 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, we substitute the given point (-8, 7) and the slope -1 into the equation:

y - 7 = -1(x - (-8))

Simplifying:

y - 7 = -1(x + 8)

Expanding:

y - 7 = -x - 8

Adding 7 to both sides:

y = -x - 1

Therefore, the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line x + y = 13 is y = -x - 1.