Write an equation of the line in standard form?

Formulas of lines have the form #y=ax+b#.

• The slope is #a#. For example, #y=5x# means that the y-coordinate increases by 5 for every #x#.
• The y-intercept is #b#. For example, #y=5x+2# has a y-intercept at the coordinates #(0,2)#.

First, write the given equations in the form #y=ax+b#.

#6x-y=5#

Subtract 6x from both sides.

#-y=5-6x#

Multiply both sides by -1.

#y=6x-5#

#4y-9x=8#

Add 9x to both sides.

#4y=9x+8#

Divide both sides by 4.

#y=2 1/4x+2#

In the first equation, #a=6# (the slope is 6). In the second equation, #b=2# (the y-intercept is 2).

Fill in the slope and the y-intercept into the #y=ax+b# form, and you've got the line #y=6x+2# or #y-6x=2# in standard form.

#6x-y=5# is a linear equation in standard form: #Ax+Bx=C#. We can find the slope by converting it to slope-intercept form: #y=mx+b#, where #m# is the slope. To convert the equation to slope-intercept form, solve for #y#.

#6x-y=5#

Subtract #6x# from both sides.

#-y=-6x+5#

Divide both sides by #-1#. This will reverse the signs.

#y=6x-5#

#m=6#

#4y-9x=8# is also in standard form. We can find the y-intercept by converting to the slope-intercept form, #y=mx+b#, where #b# is the y-intercept. Solve for #y# to convert to the slope-intercept form.

#4y-9x=8#

Add #9x# to both sides.

#4y=9x+8#

Divide both sides by #4#.

#y=9/4x+8/4#

Simplify #8/4# to #2#.

#y=9/4x+2#

#b=2#

The new equation where #m=6# and #y=2# can be written in slope-intercept form and then converted to standard form.

The new equation is:

#y=6x+2#

To convert to standard form, subtract #6x# from both sides.

#y-6x=2#