Write an Equation Given the Slope and a Point
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Slope Intercept form is y = mx + b, where
m = the slope and b = the y intercept.Slope is determined by formula
#m = (y_2  y_1)/(x_2x_1)# if you had the coordinates of two points on the line.
#(x_1,y_1) (x_2,y_2)# b is the point at which the line will cross (intercept) the yaxis.
If a problem asked for the slope intercept form and provides a slope and a single point on the line you could find the equation with two different methods.
What is the slope intercept equation of a line with a slope of m = 3/4 and a point on the line of (4 , 5)?
The first method is to us the slopeintercept equation and plug in values to solve for b.
5 =
#3/4# (4) + b (simplify the fraction)5 = 3 + b (isolate b)
5  3 = b (simplify)
b = 2
The slopeintecept equation would be y =
#3/4# x + 2The second method is to use the pointslope formula
#(y  y_1) = m(x  x_1)# Plug in the information and simplify for the equation.
#(y  5) = 3/4(x  4)# (distribute the slope)#(y  5) = 3/4x  3# (isolate y)#y = 3/4x  3 + 5# (simplify)#y = 3/4x + 2# is the slopeintercept equation. 
The slope intercept formula is,
#y=mx+b# where
#m# is the slope
where#b# is the#y# interceptThe slope is the change in y over the change in x. This is commonly known as the
#(rise)/(run)# . This is also shown as the#(Deltay)/(Deltax)# . If you have any 2 points on the line than you can also use the formula#(y_2y_1)/(x_2x_1)# .The yintercept is where the line touches or intersects the
#y# axis. If the#x# coordinate is zero you can find out what the yintercept is. 
What is xintercept? It is such an argument (xvalue) where yvalue equals 0. In equations you would tell that it is root of the equation.
In general formula
#y = mx+b# you insert known information, where#m# is a slope (or gradient) and#b# is freeterm (or yintercept  such an value where function cuts yaxis, so point (0, b) ).Let us take example. You are given slope  it is 2. And you know that your xintercept is equal 3. Therefore, you know that when
#x = 3# ,#y=0# .Let us use that information. You know that you may write every linear function like that:
#y = mx+b# .
Let us insert values:#0 = 2*3+b#
Our unknown is#b# , free term. Let us isolate it:
#b=6# .
And after all, we must insert our#b# value back into equation:#y = 2x  6# . 
No, it does not matter since you will end up with an equivalent equation.
I hope that this was helpful.
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Forms of Linear Equations

1Write an Equation Given the Slope and a Point

2Write an Equation Given Two Points

3Write a Function in SlopeIntercept Form

4Linear Equations in PointSlope Form

5Forms of Linear Equations

6Applications Using Linear Models

7Equations of Parallel Lines

8Equations of Perpendicular Lines

9Families of Lines

10Fitting Lines to Data

11Linear Interpolation and Extrapolation

12Problem Solving with Linear Models

13Dimensional Analysis