Respuesta :
Answer:
The equation of the line is 2 x - y + 5 = 0.
Step-by-step explanation:
Here the given points are A( 1, 7) & B( -3, - 1) -
Equation of a line whose points are given such that
( [tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-
y - [tex]y_{1}[/tex] = [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex] ( x - [tex]x_{1}[/tex] )
i.e. y - 7= [tex]\frac{- 1 - 7}{ -3-1}[/tex] ( x- 1)
y - 7 = [tex]\frac{- 8}{- 4}[/tex] ( x -1)
y - 7 = 2 ( x - 1)
y - 7 = 2 x - 2
2 x - y + 5 = 0
Hence the equation of the required line whose passes trough the points ( 1, 7) & ( -3, -1) is 2 x - y + 5 = 0.
The equation of line passing through the points is y = 2x + 5
Data;
- x1 = 1
- y1 = 7
- x2 = -3
- y2 = -1
Slope of a Line
To find the equation of a line, we need to know the slope of the line. This is calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's substitute the values and solve for the slope
[tex]m = \frac{-1-7}{-3-1} \\m = \frac{-8}{-4} \\m = 2[/tex]
The slope of the line is equal to 2.
Intercept of the line
The next step in solving for the equation of the line is the slope
A typical equation of line is given as
[tex]y = mx + c[/tex]
Taking one of the points;
[tex]y=mx+c\\7=2(1)+c\\7=2+c\\c= 7-2\\c= 5[/tex]
The intercept is equal to 5
The Equation of Line
The equation of a straight line is given as
[tex]y = mx + c\\[/tex]
Let's substitute the values of slope and intercept
[tex]y = mx + c\\y = 2x + 5[/tex]
The equation of line passing through the points is y = 2x + 5
Learn more on equation of line here;
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