How do you write an equation in standard form if the line passes through (3,7) and (0, -2)?

1 Answer
Apr 14, 2018

#3x - y = 2#

Explanation:

We have the value of two points, #(3, 7)# and #(0, -2)#

First, let's find the slope of this line. The formula for slope is #"rise"/"run"# or #"change in y"/"change in x"# or #(y_2-y_1)/(x_2-x_1)#.

Since we have the values of two points, we can plug them into the formula:
#(-2-7)/(0-3)#

Simplify:
#(-9)/-3#

The negatives cancel out and we simplify it:
#3#

Now we can write the equation in point-slope form, shown here:

enter image source here

#y - 7 = 3(x-3)#

To convert to standard form, we first have to convert from point-slope to slope-intercept form, shown here:
www.katesmathlessons.com

So let's simplify:
#y - 7 = 3x - 9#

Add #7# on both sides of the equation:
#y - 7 quadcolor(red)(+quad7) = 3x - 9 quadcolor(red)(+quad7)#

#y = 3x -2#

It is now in slope-intercept form.

Now let's convert this to standard form, by making the #y#-intercept by itself, shown here:
enter image source here

#y = 3x - 2#

Add #2# to both sides of the equation:
#y quadcolor(red)(+quad2) = 3x - 2 quadcolor(red)(+quad2)#

#y + 2 = 3x#

Subtract #y# on both sides of the equation:
#y + 2 quadcolor(red)(-quady) = 3x quadcolor(red)(-quady)#

#2 = 3x - y#

Switch sides to put in exact standard form:
#3x - y = 2#

As you can see, it is now in standard form.

For more information on writing an equation in standard form from two points, feel free to watch these videos:

Short video:

Longer video:

Hope this helps!