Respuesta :
The point slope form of equation through given points is:
[tex]y-6=\frac{1}{3}(x-1)[/tex]
Step-by-step explanation:
Given points are:
(x1,y1) = (-5,4)
(x2,y2) = ((1,6)
First of all we have to find the slope of line
So,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{6-4}{1+5}\\=\frac{2}{6}\\=\frac{1}{3}[/tex]
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Putting m=1/3
[tex]y-y_1=\frac{1}{3}(x-x_1)[/tex]
Putting (1,6) in the equation
[tex]y-6=\frac{1}{3}(x-1)[/tex]
The point slope form of equation through given points is:
[tex]y-6=\frac{1}{3}(x-1)[/tex]
Keywords: Point slope form
Learn more about point slope form at:
- brainly.com/question/2150928
- brainly.com/question/2154850
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Answer:
1/3 (x-1)
Step-by-step explanation:
The general point-slope form is y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)y, minus, y, start subscript, 1, end subscript, equals, m, left parenthesis, x, minus, x, start subscript, 1, end subscript, right parenthesis, where mmm is the slope and (x_1,y_1)(x
1
,y
1
)left parenthesis, x, start subscript, 1, end subscript, comma, y, start subscript, 1, end subscript, right parenthesis is a point on the line.
[Why?]
Hint #22 / 3
Let's find the slope between (\blueD{-5},\blueD{4})(−5,4)left parenthesis, start color #11accd, minus, 5, end color #11accd, comma, start color #11accd, 4, end color #11accd, right parenthesis and (\maroonD{1},\maroonD{6})(1,6)left parenthesis, start color #ca337c, 1, end color #ca337c, comma, start color #ca337c, 6, end color #ca337c, right parenthesis:
\begin{aligned} \text{Slope}&=\dfrac{\maroonD{6}-\blueD{4}}{\maroonD{1}-\blueD{(-5)}} \\\\ &=\dfrac{2}{6} \\\\ &=\dfrac{1}{3} \end{aligned}
Slope
=
1−(−5)
6−4
=
6
2
=
3
1
Hint #33 / 3
The incomplete equation starts with y-\maroonD{6}y−6y, minus, start color #ca337c, 6, end color #ca337c, so we need to use the point (\maroonD{1},\maroonD{6})(1,6)left parenthesis, start color #ca337c, 1, end color #ca337c, comma, start color #ca337c, 6, end color #ca337c, right parenthesis:
y-\maroonD{6}=\dfrac{1}{3}(x-\maroonD{1})y−6=
3
1
(x−1)
