Worksheet on Slope and Y-intercept with stepwise solutions are available here. So, the students who are all in search of the concept of slope and Y-intercept in coordinate geometry can make use of this slope and y intercept worksheets with answer key pdf and practice the problems. You can find different types of problems related to the slope (m) and y-intercept. Look into the problems given below in the slope and y intercept worksheet with answers and enhance your math skills.

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## Identifying Slope and Y Intercept Worksheet PDF

**Example 1.**

Find the slope of the line joining the points (4,−6) and (5,−2).

## Solution:

Let A(4,−8) and B(5,−2) be two points.

Slope of the line = y2 – y1/x2 – x1

= -2-(-6)/5 – 4

= -2+6/1

= 4/1

= 4

Therefore the slope of the given points are 4.

**Example 2.**

If the slope of the line joining the points A(x,3) and B(6,−8) is -6/4, find the value of x.

## Solution:

Given that the two points are

A(x,3) and B(6,-8)

x1 = x, y1 = 3, x2 = 6, y2 = -8

Given slope = -6/4

We know that

x2 – x1/y2 – y1

6 – x/-8 – 3 = -6/4

6 – x/-11 = -6/4

24 – 4x = -66

24 + 66 = 4x

90 = 4x

x = 90/4

Hence the value of x = 90/4

**Example 3.**

The following points are plotted in the x-y plane. Find the slope and y-intercept of the line joining each pair of (1,4) & (-2,3).

## Solution:

Given that the points are (1,4) and (-2,3)

x1 = 1, y1 = 4, x2 = -2 and y2 = 3

slope is (y2-y1)/(x2-x1)

(3 – 4)/(-2-1)

= -1/-3

Slope = 1/3

then y=mx+c

you get x-3y+4=0

at y axis x=0

y = 4/3

Therefore y-intercept = 4/3

**Example 4.**

Find the slope of the line, which makes an angle of 40° with the positive direction of the y-axis measured anticlockwise.

## Solution:

If a line makes an angle of 40° with the positive direction of the y-axis measured anticlockwise, then the angle made by the line with the positive direction of the x-axis measured anticlockwise is 90° +40° = 130°

Thus, the slope of the given line is

tan 130°

= tan(180° – 50°)

= −tan50°

= − 1.19175

**Example 5.**

Determine the slope and y-intercept of the line 4x + 16y + 10 = 0

## Solution:

Given that the equation is 4x + 16y + 10 = 0

16y = – 4x – 10

y = -4/16x – 10/16

y = -1/4x – 5/8.

Comparing this with y = mx + c,

Then we get m = – 1/4 and c = – 5/8

Therefore, slope = -1/4 and y-intercept = -5/8

**Example 6.**

The points (-3, 3) and (1, -4) are plotted in the x-y plane. Find the slope and y-intercept of the line joining the points.

## Solution:

Let the line graph obtained by joining the points are (-3, 3) and (1, -4) be the graph of y = mx + c.

So, the given pairs of values of (x, y) obey the relation y = mx + c.

Therefore, 3 = -3m + c …….(i)

-4 = m + c …… (ii)

Subtracting (ii) from (i),

then we get

3 + 3 = -2m – m

9 = -3m

-3m = 9

m = 9/-3

m = -3

Putting m = -3 in (ii),

Then

-4 = -3 + c

c = -1.

Now, m = -3

The slope of the line graph = -3,

c = -1

The y-intercept of the line graph = -1

**Example 7.**

Find the slope and y-intercept of 3x – √4y = 2√4

## Solution:

Given that the equation is 3x – √3y = 2√4

– √4y = -3x + 2√4

√4y = 3x – 2√4

y = 3/√4x – 2√4/√4

y = 3/√4x – 2

Comparing the above equation with y = mx + c,

Then the slope m = 3/√4 and y-intercept = -2.

**Example 8.**

Find the equation of a line in the form of y = mx + c, having a slope of 10 units and an intercept of -12 units.

## Solution:

Given that

The slope of the line, m = 10, and The y-intercept of the line, c = -12.

We know that

The slope-intercept form of the equation of a line is y = mx + c.

From the equation

y = 10x – 12

Therefore the required equation of the line is y = 10x – 12.

**Example 9.**

Determine the slope and y-intercept of the line 4y + 12 = 0

## Solution:

Given that the equation is

4y + 12 = 0

4y = -12

y = -12/4

y = 0 and x = -3

Comparing with y = mx + c,

Then we get m = 0 and c = -3

Therefore, slope = 0 and y-intercept = -3

**Example 10.**

What is the y-intercept of the graph of 2x + 7y = 6?

## Solution:

Given that the equation is 2x + 7y = 6

7y = -2x + 6

y = – 2/7x + 6/7

We know that

y = mx + c,

Comparing the equation with y = mx + c

we get c = 13/4. So, the y-intercept = 13/4

and m = -2/7 therefore slope = -2/7