What is the equation of the line between #(0,0)# and #(25,-10)#?

Question

Julia Adams · Accepted Answer

This answer will show you how to determine the slope of a line, and how to determine the point-slope, slope-intercept, and standard forms of a linear equation.

Slope First determine the slope using the formula: #m=(y_2-y_1)/(x_2-x_1),# where: #m# is the slope, #(x_1,y_1)# is one point, and #(x_2,y_2)# is the second point. Plug in the known data. I am going to use #(0,0)# as the first point, and #(25,-10)# as the second point. You can do the opposite; the slope will be the same either way. #m=(-10-0)/(25-0)# Simplify. #m=-10/25# Reduce by dividing the numerator and denominator by #5#. #m=-(10-:5)/(25-:5)# #m=-2/5# The slope is #-2/5#. Point-slope form The formula for the point-slope form of a line is: #y-y_1=m(x-x_1),# where: #m# is the slope, and #(x_1,y_1)# is the point. You can use either point from the given information. I'm going to use #(0,0)#. Again, you can use the other point. It will end up the same, but take more steps. #y-0=-2/5(x-0)# #larr# point-slope form Slope-intercept form Now we can determine the slope-intercept form: #y=mx+b,# where: #m# is the slope, and #b# is the y-intercept. Solve the point-slope form for #y#. #y-0=-2/5(x-0)# #y=-2/5x# #larr# slope-intercept form #(b=0)# Standard form We can convert the slope-intercept form into the standard form for a linear equation: #Ax+By=C,# where: #A# and #B# are integers, and #C# is the constant (y-intercept)# #y=-2/5x# Eliminate the fraction by multiplying both sides by #5#. #5y=(-2x)/color(red)cancel(color(black)(5))^1(color(red)cancel(color(black)(5)))^1# #5y=-2x# Add #2x# to both sides. #2x+5y=0# #larr# standard form graph{y=-2/5x [-10, 10, -5, 5]}

Savannah Anderson · Answer

undefined The equation of the line passing through the points $(0,0)$ and $(25,-10)$ is $y = -\frac{2}{5}x$.