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Write an equation that represents the line (-2,-6) and (2,-5)

Write an equation that represents the line (-2,-6) and (2,-5)-example-1
User Stanley Shi
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1 Answer

26 votes
26 votes

*Correction: The points given on the graph are (-2, -6) and (2, -3)

Answer:

The slope of the line is
m = (3)/(4) = 0.75

The y-intercept is
\left(0, - (9)/(2)\right) = \left(0, -4.5\right)

The equation of the line in the slope-intercept form is
y = (3 x)/(4) - (9)/(2) 0.75x−4.5

Explanation:

Your input:

Find the equation of a line given two points P=(−2,−6) and
Q = \left(2, -3\right)Q=(2,-3).

SOLUTION

The slope of a line passing through two points
P = \left(x_(1), y_(1)\right) and
Q = \left(x_(2), y_(2)\right)

is given by m =
(y_(2) - y_(1))/(x_(2) - x_(1)).

We have that ,
x_(1) = -2,
y_(1) = -6y,
x_(2) = 2x, and
y_(2) = -3y.

Plug the given values into the formula for a slope:
m = (-3 - \left(-6\right))/(2 - \left(-2\right)) = (3)/(4)

Now, the y-intercept is
b = y_(1) - m x_(1) (or
b = y_(2) - m x_(2) , the result is the same).


b=-6-((3)/(4))*(-2)=-(9)/(2)

Finally, the equation of the line can be written in the form y = b + m x:


y = (3 x)/(4) - (9)/(2)

User LuiCami
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