From Standard Form
To Slope-Intercept
Solving Equations for “y” – Part 1
Standard Form
Ax + By = C
Slope-Intercept
y = mx + b
When an equation is
in standard form:
 x and y are on the
same side of the
equal sign.
 the “A” is positive
 there are NO
fractions in the
problem.
When an equation is in
slope-intercept:
 “y” is on one side of
the equal sign and
everything else is
on the other side.
To put in slope
intercept form
means to solve the
equation for “y”.
When you solve an equation for
“y”
You are putting the equation in
“slope-intercept form”
Why do we need this formula?
y  mx  b
We use this formula to WRITE and GRAPH
linear equations.
y  mx  b
 STEPS TO SOLVE
 “x” and “y”
have to be on FOR “Y”
 Add/Subtract the
opposite
term that is on the
sides of
same side of the
equation
equation with y
 Divide by the
number in front
of y
Write these equations in slope-intercept
form.
Can’t add or sub
x  2y  8
x
x
1.
these. Why?
They are not
Like Terms
2 y   x  8
2
y
2 2
1
2
x 4
 We want y by
itself
 Mark it - then
 Move the term
beside it to the
other side (do the
opposite + or -)
 Move the term in
front of y (divide
by the number in
front of the y)
Put in Slope-Intercept Form Can’t add or sub
Solve for “y”
these.
Why?
2x  4 y  8
2x
2x
2.
They are not
Like Terms
4 y  2 x  8
4
4 4
1
y  x2
2
 We want y by
itself
 Mark it - then
 Move the term
beside it to the
other side (do the
opposite + or -)
 Move the term in
front of y (divide
by the number in
front of the y)
Put in Slope-Intercept Form Solve for “y”
3.
4x  2 y  8
4x
4x
2 y  4x  8
2
2
y  2x 4
2
 We want y by
itself
 Mark it - then
 Move the term
beside it to the
other side (do the
opposite + or -)
 Move the term in
front of y (divide
by the number in
front of the y)
Put in Slope-Intercept Form Solve for “y”
4.
4x  y  6
6
6
4x  6  y
y  4x  6
5. 5 x  y  3
3
3
5x  3  y
y  5x  3
 We want y by
itself
 Mark it - then
 Move the term
beside it to the
other side (do the
opposite + or -)
 Move the term in
front of y (divide
by the number in
front of the y)
 Nothing to move!!
So turn it around!
Put in Slope-Intercept Form Solve for “y”
6.
2 y  8 x  12
7.
4 y  12 x  16
2 2 2
y  4x 6
4 4 4
y  3x 4
 We want y by itself
 Mark it - then
 Move the term
beside it to the
other side (do the
opposite + or -)
 Nothing to move so
 Move the term in
front of y (divide by
the number in front
of the y)
Now let’s use the formula to
WRITE an equation.
y  mx  b
Write an equation in slope-intercept form when given the
slope and the y-intercept.
8. m = 3, b = 1
1
y  __
3 x  __
y  3x  1
Simply replace the “m” and the “b”
in the formula with the numbers
and you have an equation.
Write an equation in slope-intercept form when given the
slope and the y-intercept.
Writing Slope-Intercept Equations - Examples
y  __ x  __
9. m = -3, b = 5
y  3x  5
11. m = 0, b = 7
y  0x  7
y7
10. m = ½ , b = 1
1
y  x 1
2
12. m = 4, b = -2
y  4x  2