Answer:
The equation of line with given slope that include given points is 3 y + x - 20 = 0
Step-by-step explanation:
According to Cora , if we know the slope and points on a line then we can write the equation of a line .
Since , The equation of line in slope-intercept form is
y = m x + c
Where m is the slope of line , and if we know the points ( x , y ) which satisfy the line then constant term c can be get and the equation of line can be formed .
So , From the statement said above it is clear that she is correct .
Now , Again
Given as :
Slope of a line is m = - [tex]\frac{1}{3}[/tex]
That include points ( 2 , 6 )
Now from the equation of line as y = m x + c
∴ 6 = - [tex]\frac{1}{3}[/tex] ( 2 ) + c
Or, 6 = - [tex]\frac{2}{3}[/tex] + c
So , c = 6 + [tex]\frac{2}{3}[/tex]
or, c = [tex]\frac{18 + 2}{3}[/tex]
∴ c = [tex]\frac{20}{3}[/tex]
So, The equation of line can be written as
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{20}{3}[/tex]
Or, 3 y = - x + 20
I.e 3 y + x - 20 = 0
Hence The equation of line with given slope that include given points is 3 y + x - 20 = 0 Answer
