A line passes through the point (-6, 6) and (-6, 2). In two or more complete sentences, explain why it is not possible to write the equation of the given line in the traditional version of the point-slope form of a line. please answer asap
Answers
Answer:
There are three main forms of linear equations.
Slope-intercept Point-slope Standard
y=\maroonC mx+\greenD by=mx+by, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #1fab54, b, end color #1fab54 y-\purpleD{y_1}=\maroonC m(x-\purpleD{x_1})y−y
1
=m(x−x
1
)y, minus, start color #7854ab, y, start subscript, 1, end subscript, end color #7854ab, equals, start color #ed5fa6, m, end color #ed5fa6, left parenthesis, x, minus, start color #7854ab, x, start subscript, 1, end subscript, end color #7854ab, right parenthesis Ax+By=CAx+By=CA, x, plus, B, y, equals, C
where \maroonC{m}mstart color #ed5fa6, m, end color #ed5fa6 is slope and \greenD{b}bstart color #1fab54, b, end color #1fab54 is the yyy-intercept where \maroonC{m}mstart color #ed5fa6, m, end color #ed5fa6 is slope and \purpleD{(x_1,y_1)}(x
1
,y
1
)start color #7854ab, left parenthesis, x, start subscript, 1, end subscript, comma, y, start subscript, 1, end subscript, right parenthesis, end color #7854ab is a point on the line where AAA, BBB, and CCC are constants
Example
A line passes through the points (-2,-4)(−2,−4)left parenthesis, minus, 2, comma, minus, 4, right parenthesis and (-5,5)(−5,5)left parenthesis, minus, 5, comma, 5, right parenthesis. Find the equation of the line in all three forms listed above.
Two of the forms require slope, so let's find that first.
\begin{aligned} \text{slope}=\maroonC m &= \dfrac{\Delta y}{\Delta x}\\\\ &=\dfrac{5-(-4)}{-5-(-2)}\\\\ &=\dfrac{9}{-3} \\\\ &=\maroonC{-3} \end{aligned}
slope=m
=
Δx
Δy
=
−5−(−2)
5−(−4)
=
−3
9
=−3