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Question 291685: Please help me, i am dumbfounded by this question!!!
Write an equation in point slope form of the line that goes through the point (-9,-3) and has a slope of 3/4.
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! Point slope form of an equation is described in this reference:
http://www.freemathhelp.com/point-slope.html
The standard form of the point slope form of the equation of a line is:
(y-y1) = m*(x-x1)
(x1,y1) is the set of points you are given.
m is the slope.
You are given that the slope is equal to (3/4).
you are given that the point (x1,y1) is (-9,-3)
Substitute in the standard form of the point slope form of the equation to get:
(y-(-3)) = (3/4) * (x-(-9))
Since a minus of a minus is a plus, this becomes:
(y+3) = (3/4) * (x+9)
That's the point slope form of the equation of your line.
To graph this equation, you have to convert the point slope form of the equation into the slope intercept form of the equation.
The standard form of the slope intercept form of the equation of a line is:
y = m*x + b, where:
m is the slope and b is the y intercept.
You convert your point slope form of the equation into the slope intercept form of the equation by solving for y.
Your point slope form of the equation is:
(y+3) = (3/4) * (x+9)
Simplify this equation to get:
y + 3 = (3/4)*x + (3/4)*9
Simplify further to get:
y + 3 = (3/4)*x + (27/4)
Subtract 3 from both sides of this equation to get:
y = (3/4)*x + (27/4) - 3
Since 3 is the same as (12/4), this equation becomes:
y = (3/4)*x + (27/4) - (12/4) which becomes:
y = (3/4)*x + (15/4).
This is the slope intercept form of your equation which can now be graphed.
The graph of this equation is shown below:
I drew a horizontal line at y = (15/4) to show you that the value of y when x = 0 is (15/4). The value of y when x equals 0 is the y intercept.
I drew a horizontal line at y = -3 to show you that the value of x when y = -3 is x = -9 which corresponds to the point (-9,-3) that you were given.
the slope is (3/4) can be confirmed because for every change in y value of 3, you should see a change in the x value of 4.
For example:
When x = 0, y = (3/4)*0 + (15/4) = (15/4) which is equivalent to 3.75
When x = 4, y = (3/4)*4 + (15/4) = 3 + (15/4) = (27/4) which is equivalent to 6.75 which is 3 more than 3.75.
Your y value changed 3 units when your x value changed 4 units.
Slope is a change in y value divided by a change in x value = (3/4).
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