Answer:
Step-by-step explanation:
consider that (x,y) is a general point on the line (variable), and (x1, y1) is a given fixed point on the line
M, the slope of the line may be given as:
M = (y - y1) / (x - x1)
if you know the value of M, and the values x1 and y1, (which you do, since point (x1, y1) is given to you as a fixed point),
you can rearrange the above equation to get the equation of the line
the reason for this is that every point (x,y) on the required line will satisfy the above equation ( (x,y) is a general point )
which means this equation is a relation between x and y which gives us the values of x and y which make (x,y) fall on the line
this means that the obtained relation is nothing but a representation of the required line, ie equation of the line
in the second example, fixed point is (x1, y1) =(1, 0)
M = (-4)
x1 = 1
y1 = 0
we have,
M = (y - y1) / (x - x1)
ie (-4) = (y - 0) / (x - 1)
ie (-4) = y / (x-1)
ie y = -4x + 4
ie [ 4x + y = 4 ]
which is the equation of the line
the first example is almost the same thing
onlhy in this case you have to find the slope M manually
M = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are given fixed points on the line
in the example,
M = [ 5 - (-3) ] / [ 3 - 2 ]
M = 8 / 1
M = 8
and proceed in a manner similar to the other example
Answer:
x = 1
Step-by-step explanation:
8x - 19 = -4 - 7x
Combine x's on one side of the equation and constants on the other side.
8x + 7x = -4 + 19
15x = 15
Divide both sides by 15
x = 1
