Question #76df0

2 Answers
Dec 18, 2016

Answer:

The equation would be #y = mx + b#

Explanation:

B is the y intercept, the point of the line that touches some part of the y-axis.

M is the slope (rise over run). You find it by plugging two points on the line into the slope equation: #m = (y_2 - y_1)/(X_2 - x_1)#.

Y is basically the linear function.

So if I have a line with the equation: #y = 2x + 1#

I can plug in values for #x# and #y# (let's say 1). I replace #x# with 1 so --> #y = 2(1) + 1#. SO if #x# is 1, then I can solve the equation and say #y = 3#. That's one point (1, 3) on the line of the equation above. Another value to find another point. #b# is 1 because #y# = 2#x# + 1. That means at (x, #1#) the line touches the y-axis.

And as I gave the equations above, when you find the second coordinate (the first being (1, 3)) by plugging in another value for #x# and solving for #y#, you can find #m#, the slope.

Dec 18, 2016

Perhaps the question refers to the "intercept form" of a line:

#x/a +y/b=1#,
where the #x# intercept is #(a,0)# and the #y# intercept is #(0,b)#.

To convert this form to slope intercept form #y=mx+b# (where #m# is the slope and #b# is the #y# intercept),

multiply the equation #x/a +y/b=1# by the LCD #ab#

#ab(x/a +y/b =1)#

#(abx)/a +(aby)/b=ab#

#bx+ay=ab#
#-bxcolor(white)(aaa)-bx#

#ay=-bx+ab#

#(ay)/a=(-bx)/a+(ab)/a#

#y=(-b/a)x +b#

So, to convert from the "intercept form" of a line #x/a+y/b=1#
to the "slope intercept form" #y=mx+b#,

the slope #m=-b/a# and the y intercept #b# is equal to the "b" in the intercept form.