SOLUTION: find the slope and the y-intercept of the line whose equation is 2x+3y=12 and another question write an equation of the line through (1,-3) and (-2,6)

Question 86175: find the slope and the y-intercept of the line whose equation is 2x+3y=12
and another question
write an equation of the line through (1,-3) and (-2,6)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

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

Start with the given equation

Subtract 2x from both sides

Simplify

Divide both sides by 3 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

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

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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.

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