Write the equation of the line, in slope-intercept form, that passes through the point (-2, -1) and has slope 5.
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Answer:
The x co-ordinate o intersection of line k and n is
Step-by-step explanation:
Given as :
The equation of line m is 6 x - 3 y = 7
So, in the standard form , line equation is
y = a x + c , where a is the slope
So, 6 x - 3 y = 7 can be written as
3 y = 6 x - 7
or, y = 2 x - ........1
So, slope of this line = a = 2
Now, The line n is perpendicular to line m and passing through line ( 6 , 2 )
So, Slope of line n = b
For , perpendicular lines , products of slope = - 1
Or, a × b = -1
∴ b = -
I.e b = -
So,equation of line n with slope b and passing through line ( 6 , 2 ) is
y - = b ( x -
)
or, y - 2 = - ( x - 6 )
or, 2 × ( y - 2 ) = - 1 ( x - 6 )
or, 2 y - 4 = - x + 6
or, x + 2 y -10 = 0 ........2
Again, equation of line k with slope 5 and y intercept = 1
For y intercept , x coordinate = 0
y = c x + c
or, 1 = c× ( 0 ) + c
Or, c = 1
Or, equation of line k is
y = 5 x + 1 ..........3
Now intersection of line k and n is
put the value of y from eq 3 into eq 2
I.e x + 2 × ( 5 x + 1 )-10 = 0
Or, x + 10 x + 2 - 10 = 0
or, 11 x - 8 = 0
or 11 x = 8
∴ x =
Hence The x co-ordinate o intersection of line k and n is Answer