1. Standard form and Point-slope form of linear equations
Define and use the standard form of a linear equation.
Define and use the point-slope form of a linear equation.

2. Standard Form of a linear equation: Ax + By = C
In this form, the x and y are on one side of the equal sign and the constant ( the number without the variable) is one the other side.
Generally, A, the coefficient of x, is written as a POSITIVE WHOLE NUMBER.
An equation in slope-intercept form can be converted into standard form: y = -6x+8
 Slope-intercept form. The y is by itself with a coefficient of 1.
6x+y = 8
 Standard form. The x and y are on one side. x has a positive whole number coefficient

3. Point Slope form: y - y1 = m(x - x1)
You plug the values of the coordinates of a given point into the x1 & y1 spots and the slope into the m spot.
Write an equation in point slope form for a line that has a slope of 4 and contains the point (-3, 8)
y - y1 = m(x - x1)
y - 8 = 4(x - -3)
y - 8 = 4(x + 3)

4. Write an equation in point slope form for the line that contains (5,-2) & (-2,5)
y1 - y2 x1 - x2
-2-5
5- -2
= -7 7
=-1
Step 1) find the slope:
Step 2) use that slope you found and either one of the points and plug it into the equation
y - y1 = m(x - x1)
y - 5 = -1(x - -2)
y - 5 = -1(x +2)
y - y1 = m(x - x1)
y - -2 = -1(x - 5) or
y + 2 = -1(x -5)

5. But are these equations the same?
y - 5 = -1(x +2)
y + 2 = -1(x -5)
Get them into slope-intercept form to see if they are the same
y - 5 = -1(x +2)
y-5 =-x-2
y=-x+3
y + 2 = -1(x -5)
y+2=-x+5
y=-x+3
Or get them into standard form to see if they are the same
y - 5 = -1(x +2)
y-5 = -x-2
x+y-5 = -2
x+y = 3
y + 2 = -1(x -5)
y+2=-x+5
x+y+2 = 5
x+y = 3

6. Find the x- & y-intercepts for the graph of the equation: 4x-5y=20
Since it is not in slope-intercept form you cannot just read the y-intercept. You must solve the problem twice. Plug in a zero, one at a time, for each variable.
4x-5y=20
4x-5y=20
4(0)-5y=20
4x-5(0)=20
-5y=20
4x =20
x=5
y= -4
y-intercept is (0,-4)
x-intercept is (5,0)