FIND SLOPE AND Y INTERCEPT FROM THE EQUATION

Find slope and y intercept of the line given below.

Problem 1 :

x + 4y = 8

Solution :

x + 4y = 8

The given equation is in standard form, to convert this equation to slope intercept form.

4y = - x + 8

Divide each side by 4.

y = -x/4 + 8/4

y = (-1/2) x + 2

The above equation is in the form y = mx + b

Then,

Slope (m) = -1/2  

y-intercept (b) = 2

Problem 2 :

2x - 6y = -12

Solution :

2x - 6y = -12

-6y = -2x - 12

Divide each side by -6.

y = (-2/-6) x + (-12/-6)

y = (1/3) x + 2

The above equation is in the form y = mx + b

Then,

Slope (m) = 1/3

y-intercept (b) = 2

Problem 3 :

y = - 2

Solution :

y = 0x - 2

The above equation is in the form y = mx + b

Then,

Slope (m) = 0

y-intercept (b) = - 2

Problem 4 :     

5x - y = 3

Solution :

5x - y = 3

-y = - 5x + 3

y = 5x - 3

The above equation is in the form y = mx + b

Then,

Slope (m) = 5

y-intercept (b) = - 3

Problem 5 :

-5x + 10y = 20

Solution :

-5x + 10y = 20

10y = 5x + 20

Divide each side by 10.

y = (5/10) x + (20/10)

y = (1/2) x + 2

The above equation is in the form y = mx + b

Then,

Slope (m) = 1/2

y-intercept (b) = 2

Problem 6 :

-x - y = 6

Solution :

-x - y = 6

-y = x + 6

y = - x - 6

The above equation is in the form y = mx + b

Then,

Slope (m) = - 1

y-intercept (b) = - 6

Problem 7 :

2.5x - 5y = - 15

Solution :

2.5x - 5y = - 15

-5y = -2.5x - 15

5y = 2.5x + 15

Divide each side by 5.

y = (2.5/5) x + (15/5)

y = 0.5 x + 3

The above equation is in the form y = mx + b

Then,

Slope (m) = 0.5

y-intercept (b) = 3

Problem 8 :

x = - 5/2

Solution :

x = - 5/2

Since x = - 5/2 is a vertical line, there is no y-intercept and the slope is undefined.

Problem 9 :

Write the equation of the line passes through the point (0, 5) and is parallel to the graph of y = 7x + 4 in the xy-plane?

Solution :

y = 7x + 4

When the lines are parallel, their slopes will be equal.

m = 7

It passes through the point (0, 5)

y = mx + b

y = 7x + b

y-intercept (b) = 5

y = 7x + 5

Problem 10 :

The total cost f(x) in dollars to lease a car for 6 months from a particular car dealership is given by f(x) = 36x + 1000, where x is the monthly payment in dollars. What is the total cost to lease a car when the monthly payment is $400 ?

a)  $13400   b)  $13000     c)  $15400     d)  $37400

Solution :

f(x) = 36x + 1000

Monthly payment = $400

To find the total cost, let us apply x = 400

f(400) = 36(400) + 1000

= 14400 + 1000

= 15400

So, the required cost is $15400, option c is correct.

Problem 11 :

The function h is defined by h(x) = 4x + 28. The graph of y = h(x) in the xy-plane has an x-intercept at (a, 0) and a y-intercept is at (0, b), what is the value of a and b are constants. Waht is hte value of a + b ?

a)  21      b)  28     c)  32     d)  35

Solution :

h(x) = 4x + 28

Let y = 4x + 28

To find x-intercept, we put y = 0

0 = 4x + 28

4x = -28

x = -28/4

x = -7

To find the y-intercept, we put x = 0

y = 4(0) + 28

y = 0 + 28

y = 28

a = -7 and b = 28

a + b = -7 + 28

= 21

The vlaue of a + b is 21. Option a is correct.

Problem 12 :

g(m) = -0.05m + 12.1

The given function g models the number of gallons of gasoline that remains from a full gas tank in a car after driving m miles. According to the model, about how many gallons of gasoline are used to drive each mile?

a)  0.05      b)  12.1    c)  20     d)  242

Solution :

g(m) = -0.05m + 12.1

Comparing the equation with y = mx + b

m = -0.05

To drive each mile 0.05 gallons of gasoline is used.