SOLUTION: find the slope of the line that passes through (-3,1) and (2,-6). find an equation of each line in standard form satisfying the given conditions.

Question 106865This question is from textbook intermediate algebra
: find the slope of the line that passes through (-3,1) and (2,-6).
find an equation of each line in standard form satisfying the given conditions. This question is from textbook intermediate algebra

Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

So the slope is

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Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Distribute

Multiply and to get

Add to both sides to isolate y

Combine like terms and to get (note: if you need help with combining fractions, check out this solver)

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.

Now let's convert the slope-intercept equation into standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)

Start with the given equation

Multiply both sides by the LCD 5

Distribute and multiply

Add 7x to both sides

Simplify

The original equation (slope-intercept form) is equivalent to (standard form where A > 0)

The equation is in the form where , and

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
find the of the line that passes through (,) and (,).

If , , , then we have:
m =(y[2] � y[1])/(x[2] � x[1])
Since

we will have:
m = (-6� 1)/(2 � (-3))

We are trying to find equation .
The value of slope is already given to us, as a point (,) that lies on the line as well.
we need which is:
�

so,
will be:

here is the graph of this function, make sure that both given points (,) and (,)lie on line.

Solved by pluggable solver: Graphing Linear Equations

In order to graph we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-8

Multiply

Add

So here's one point (-8,8)

Now lets find another point

Plug in x=2

Multiply

Add

So here's another point (2,-6). Add this to our graph

Now draw a line through these points

So this is the graph of through the points (-8,8) and (2,-6)

So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go down -1.4 units and to the right 1 units to get to the next point), the y-intercept is (0,)and the x-intercept is (,0)

We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,).

So we have one point (0,)

Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go down 1.4 units

and to the right 1 units to get to our next point

Now draw a line through those points to graph

So this is the graph of through the points (0,-3.2) and (1,-4.6)

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