How do you write an equation of a line given slope is 3/7 and the ordered pair is (0, 5/6)?

3 Answers
Jul 15, 2016

#y=3/7x+5/6#

Explanation:

#color(red)("Step 1")#
The general equation of a straight line is: #y=mx+c#

Where #m# is the gradient and #c# is a constant which is also the y-intercept.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Step 2")#

We are told that the gradient (slope) is #3/7# so by substituting this for #m# we have

#y=3/7x+c#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(red)("Step 3")#

We are given a condition where this equation is true. We are told that it passes through the point #(x,y)->(color(blue)(0,5/6))#

So we van substitute for both #x# and #y# to determine the value of #c#.

#color(brown)(y=3/7x+x" "->" "color(blue)(5/6)=3/7(color(blue)(0))+c)#

But #7/7xx0=0# giving:

#5/6=c#

Thus the finished equation is:

#y=3/7x+5/6#

Tony P

Jul 15, 2016

#y = 3/7x +5/6#

Explanation:

There is a nifty formula for the equation of a line which applies in just such a case where we are given the slope and one point.

Using this formula requires only ONE step with substitution and some easy simplifying. Works like a dream...

#y-y_1 = m(x-x_1)" m = slope and "(x_1,y_1)" is a point"#

#y -5/6 = 3/7(x-0)#

#y = 3/7x +5/6#

However, in this particular case, no working was required at all.

The slope, m is given as #3/7# and the point given happens to be the y-intercept because the #x-#value is 0. So #c = 5/6#

#y = mx + c rArr y = 3/7x +5/6#

Jul 15, 2016

Alternative approach

#y=3/7x+5/6#

Explanation:

Let the slope (gradient) be #m#

The gradient (slope) the change in up or down for a given change in along.

#m=("Change in y")/("Change in x") = 3/7#

Let given point be #P_o->(x_o,y_o) = (0,5/6)#

Let any other point be #P_i->(x_i,y_i)#

Then #m=("Change in y")/("Change in x") -> (y_i-y_o)/(x_i-x_o) = (y_i-5/6)/(x_i-0) = 3/7#

#y_i=3/7x_i+5/6#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#y=3/7x+5/6#