Given equation of line is
we can rewrite it as
Now, we know that
In this problem A = 4 , B = 3 C = -12 and d = 4
point is on x-axis therefore = (x ,0)
Now,
Now if x > 3
Then,
Therefore, point is (8,0)
and if x < 3
Then,
Therefore, point is (-2,0)
Therefore, the points on the x-axis, whose distances from the line are units are (8 , 0) and (-2 , 0)

Given the equation of the line is
we can rewrite it as
Now, we know that
where A and B are the coefficients of x and y and C is some constant and is point from which we need to find the distance
In this problem A = 12 , B = -5 , c = 82 and = (-1 , 1)
Therefore,
Therefore, the distance of the point from the line is 5 units

Given equation is
Coefficient of x is 1 and y is -1
Therefore,
Now, Divide both the sides by
we wiil get
we can rewrite it as
Now, we know that normal form of line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On compairing equation (i) and (ii)
we wiil get
Therefore, the angle between perpendicular...

Given equation is
we can rewrite it as
Coefficient of x is 0 and y is 1
Therefore,
Now, Divide both the sides by 1
we will get
we can rewrite it as
Now, we know that normal form of line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On comparing equation (i) and (ii)
we wiil get
Therefore, the...

Given equation is
we can rewrite it as
Coefficient of x is -1 and y is
Therefore,
Now, Divide both the sides by 2
we will get
we can rewrite it as
Now, we know that the normal form of the line is
Where is the angle between perpendicular and the positive x-axis and p is the perpendicular distance from the origin
On comparing equation (i) and (ii)
we wiil get
Therefore, the...

**Q: 2 ** Reduce the following equations into intercept form and find their intercepts on the axes.

(iii)

Given equation is
we can rewrite it as
Therefore, intercepts on y-axis are
and there is no intercept on x-axis

**Q : 2 ** Reduce the following equations into intercept form and find their intercepts on the axes.

(ii)

Given equation is
we can rewrite it as
-(i)
Now, we know that the intercept form of line is
-(ii)
Where a and b are intercepts on x and y axis respectively
On comparing equation (i) and (ii)
we will get
and
Therefore, intercepts on x and y axis are and -2 respectively

Given equation is
we can rewrite it as
-(i)
Now, we know that the intercept form of line is
-(ii)
Where a and b are intercepts on x and y axis respectively
On comparing equation (i) and (ii)
we will get
a = 4 and b = 6
Therefore, intercepts on x and y axis are 4 and 6 respectively

Given equation is
-(i)
Now, we know that the Slope-intercept form of the line is
-(ii)
Where m is the slope and C is some constant
On comparing equation (i) with equation (ii)
we will get
and
Therefore, slope and y-intercept are respectively

Given equation is
we can rewrite it as
-(i)
Now, we know that the Slope-intercept form of line is
-(ii)
Where m is the slope and C is some constant
On comparing equation (i) with equation (ii)
we will get
and
Therefore, slope and y-intercept are respectively

Given equation is
we can rewrite it as
-(i)
Now, we know that the Slope-intercept form of the line is
-(ii)
Where m is the slope and C is some constant
On comparing equation (i) with equation (ii)
we will get
and
Therefore, slope and y-intercept are respectively

Points are collinear means they lies on same line
Now, given points are and
Equation of line passing through point A and B is
Therefore, the equation of line passing through A and B is
Now, Equation of line passing through point B and C is
Therefore, Equation of line passing through point B and C is
When can clearly see that Equation of line passing through point A nd B ...

Let the coordinates of Point A is (x,0) and of point B is (0,y)
It is given that point R(h , k) divides the line segment between the axes in the ratio
Therefore,
R(h , k)
Therefore, coordinates of point A is and of point B is
Now, slope of line passing through points and is
Now, equation of line passing through point and with slope is
Therefore, the equation of line is

Now, let coordinates of point A is (0 , y) and of point B is (x , 0)
The,
Therefore, the coordinates of point A is (0 , 2b) and of point B is (2a , 0)
Now, slope of line passing through points (0,2b) and (2a,0) is
Now, equation of line passing through point (2a,0) and with slope is
Hence proved

It is given that the owner of a milk store sell
980 litres milk each week at
and litres of milk each week at
Now, if we assume the rate of milk as x-axis and Litres of milk as y-axis
Then, we will get coordinates of two points i.e. (14, 980) and (16, 1220)
Now, the relation between litres of milk and Rs/litres is given by equation
Now, at he could sell
He could sell...

It is given that
If then
and If then
Now, if assume C along x-axis and L along y-axis
Then, we will get coordinates of two points (20 , 124.942) and (110 , 125.134)
Now, the relation between C and L is given by equation
Which is the required relation

Let the slope of the line is m
and slope of a perpendicular line is which passes through the origin (0, 0) and (-2, 9) is
Now, the slope of the line is
Now, the equation of line passes through the point (-2, 9) and with slope is
Therefore, the equation of the line is

We know that
Now, equation of line passing through point (0 , 2) and with slope is
Therefore, equation of line is -(i)
Now, It is given that line crossing the -axis at a distance of units below the origin which means coordinates are (0 ,-2)
This line is parallel to above line which means slope of both the lines are equal
Now, equation of line passing through point...

Let (a, b) are the intercept on x and y axis respectively
Then, the equation of line is given by
It is given that
a + b = 9
b = 9 - a
Now,
It is given that line passes through point (2 ,2)
So,
case (i) a = 6 b = 3
case (ii) a = 3 , b = 6
Therefore, equation of line is 2x + y = 6 , x + 2y = 6

Let (a, b) are the intercept on x and y-axis respectively
Then, the equation of the line is given by
Intercepts are equal which means a = b
Now, it is given that line passes through the point (2,3)
Therefore,
therefore, equation of the line is

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