FINDING SLOPE AND Y INTERCEPT FROM THE GIVEN EQUATION

Question 1 :

Find the slope and y-intercept of the line whose equation is y = x + 1.

Solution : 

To find the slope and y-intercept of any line, we have to compare the given equation with y = mx + c.

Here m stands for slope and c stands for y-intercept.

y = x + 1

y = mx + c

Comparing y = x  + 1 to y = mx + c, we get

slope (m)  =  1

y-intercept (c)  =  1

Question 2 :

Find the slope and y-intercept of the line whose equation is 5x = 3y.

Solution :

3y  =  5x 

y = (5/3)x

Then,

Slope (m)  =  5/3

y-intercept (c)  =  0

Question 3 :

Find the slope and y-intercept of the line whose equation is 4x - 2y + 1 = 0

Solution :

2y = 4x + 1

y = (4/2)x + (1/2) 

y = 2 x + (1/2)

Then,

slope (m)  =  2

y-intercept (c)  =  1/2

Question 4 :

Find the slope and y-intercept of the line whose equation is 10x + 15y + 6 = 0.

Solution :

15y = -10x - 6 

y = (-10/15)x - (6/15) 

y = (-2/3) x - (2/5)

Then,

slope m  =  -2/3

y-intercept (c)  =  2/5

Question 5 :

Find the equation of the straight line whose slope is -4 and passing through (1, 2).

Solution :

Slope (m)  = -4  and  (x₁, y₁)  =  (1, 2).

(y - y₁)  =  m(x - x₁)

(y - 2)  =  -4(x - 1)

y - 2  =  -4x + 4 

4x + y - 2 - 4  =  0

4x + y - 6  =  0

Question 6 :

Find the equation of the straight line whose slope slope is 2/3 and passing through (5, -4).

Solution :

Slope (m)  =  2/3, (x₁, y₁)  =  (5, -4).

(y - y₁)  =  m (x - x₁)

(y - (-4)) =  (2/3)(x - 5)

(y + 4) = (2/3) (x - 5)

3(y + 4) = 2(x - 5)

3y + 12 = 2x - 10

2x - 3y - 10 - 12 = 0

2x - 3y - 22 = 0

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