What is the slope of the line #-2x-5y=11#?

2 Answers
May 26, 2017

Answer:

See a solution process below:

Explanation:

We can transform this line to the Standard Form for Linear Equations. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform this equation we need to multiply each side of the equation by #color(red)(-1)# to ensure the coefficient for #x# is positive while keeping the equation balanced:

#color(red)(-1)(-2x - 5y) = color(red)(-1) xx 11#

#(color(red)(-1) xx -2x) + (color(red)(-1) xx - 5y) = -11#

#color(red)(2)x + color(blue)(5)y = color(green)(-11)#

The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#

Substituting the #x# and #y# coefficients gives:

#m = -color(red)(2)/color(blue)(5)#

May 26, 2017

Answer:

The slope is #-2/5#.

Explanation:

Find the slope:

#-2x-5y=11#

Solve for #y#, which will give you the slope intercept form of a linear equation: #y=mx+b#, where #m# is the slope and #b# is the y-intercept.

Add #2x# to both sides of the equation.

#-color(red)cancel(color(black)(2x))+color(red)cancel(color(black)(2x))-5y=2x+11#

Simplify.

#-5y=2x+11#

Divide both sides by #-5#.

#(color(red)cancel(color(black)(-5))y)/(color(red)cancel(color(black)(-5)))=-2/5x-11/5#

Slope intercept form.

#y=-2/5x-11#

The slope is #-2/5#