SOLUTION: Hello out there,I need some help with some slope problems that is giving me a hard time,the first one is,Write the point-slope form of the line that passes through (3,-3)and (5,1).

Question 82171: Hello out there,I need some help with some slope problems that is giving me a hard time,the first one is,Write the point-slope form of the line that passes through (3,-3)and (5,1).The second one is,Write an equation in slope-intercept form of the line having the given slope and passing through the given point:m=o,(0,-3).The next one is,Write the equation in slope-intercept form of the passing through each pair of points:(6,-2)and (3,-4).The last one is,Write the equation in slope-intercept form of the line passing through each pair of points:(-8,2)and (0,6),thanks for whoever can help.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
note: if you need more help with finding an equation through 2 points check out this solver

"Write the point-slope form of the line that passes through (3,-3)and (5,1)"

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

Reduce

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 . Now reduce to get

Subtract from both sides to isolate y

Combine like terms and to get

------------------------------------------------------------------------------------------------------------

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.

"The second one is,Write an equation in slope-intercept form of the line having the given slope and passing through the given point:m=0,(0,-3)"

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

it goes through point (0, -3)

it has a slope of 0

First, let's draw a diagram of the coordinate system with point (0, -3) plotted with a little blue dot:

Write this down: the formula for the equation, given point and intercept a, is

(see a paragraph below explaining why this formula is correct)

Given that a=0, and , we have the equation of the line:

Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: .

Here's the graph:

note: its hard to see, but its a horizontal line going through (0,-3)

"The next one is,Write the equation in slope-intercept form of the passing through each pair of points:(6,-2)and (3,-4)"

Solved by pluggable solver: Finding the Equation of a Line

"Write the equation in slope-intercept form of the line passing through each pair of points:(-8,2)and (0,6)"

Solved by pluggable solver: Finding the Equation of a Line

------------------------------------------------

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 . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

------------------------------------------------------------------------------------------------------------

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.

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