How do you find the slope and intercept of #y-3/5x=-1/4#?

1 Answer
Mar 9, 2016

Answer:

Slope: #3/5#
y-intercept: #-1/4#
x-intercept: #5/12#

Explanation:

A way to find the slope and intercepts of a linear equation is to transform it into the slope-intercept form. Generally the slope-intercept form looks like this:

#y = mx + b#

Where m is the slope and b is the y-intercept.

In this case, the given is #y - 3/5x = -1/4#, so we just have to transpose the term with the #x# variable into the other side of the equation.

[Solution]
#y - 3/5x = -1/4#
#y = 3/5x - 1/4#

Now that we have the slope-intercept form, we know from the equation that...

Slope -> #m = 3/5#
y-intercept: #-1/4#

As for the x-intercept, we know that when the graph crosses the x-axis then the value of #y# is 0. So in order to compute for the x-intercept, we only need to evaluate the equation with #y = 0#.

[Solution]
#y - 3/5x = -1/4#
#0 - 3/5x = -1/4#
#-3/5x = -1/4#
#3/5x = 1/4#
#x = (1/4)(5/3)#
#x = 5/12#