How do you graph the line that passes through the origin parallel to the line x+y=10?

1 Answer
May 29, 2017

Answer:

See a solution process below:

Explanation:

The equation in the problem is in Standard Form for a Linear Equation. 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

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

Therefore, #color(red)(1)x + color(blue)(1)y = color(green)(10)# has slope:

#m = -color(red)(1)/color(blue)(1) = -1#

A line parallel to this line will, by definition have the same slope.

We know the #y# intercept is #0# because the line passes through the origin therefore when #x = 0#, #y = 0#

We can use the slope-intercept formula to write and equation:

The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Substituting the slope we calculated and the #y#-intercept from the point in the problem gives:

#y = color(red)(-1)x + color(blue)(0)#

Or

#y = color(red)(-1)x#

We can also solve for the Standard Form:

#x + y = x + color(red)(-1)x#

#color(red)(1)x + color(blue)(1)y = 0#

Or

#x + y = 0#