The general equation of line with passing points (a, b) and slope m is :
y = m(x - a) + b
In the given question :
A line goes through the point (2,1)
Passing point (a, b) = (2, 1)
a slope of 2
Slope : m = 2
Substitute these value in the general equation of line :
y = m( x - a ) + b
y = 2 ( x - 2) + 1
y = 2x - 4 + 1
y = 2x - 3
y = 2x - 3
A)
To plot on the graph :
We have one coordinate ( 2, 1)
Find one more coordinate
Substitute x = 1 in the equation os line :
y = 2x - 3
y = 2(1) - 3
y = ( - 1 )
So, (x, y) = ( 1, -1)
Plot the coordinates ( 2, 1) & ( 1, - 1)
y- intercept is the point on the line where x = o
Substitute x = 0 in the given equation of line :
y = 2x - 3
y = 2( 0 ) - 3
y = ( -3 )
Y -intercept : y = ( -3) , (x, y) = ( 0, -3)
In the graph y -intercept is :
The purple point in the graph represent the y -intercept.
B)
The general form of the equation of line in the form of slope intercept form :
y = mx + b
The equation of line y = 2x - 3
On compare with the general equation of slope intercept form we have : m - 2, b = (-3)
So, equation of line in the slope intercept form is : y = 2x - 3
y = 2x - 3
Answer : A) ( x, y) = (0, -3)
B) y = 2x - 3