Problems on Slope and Y-intercept with step-by-step explanations are available here. The equation of the slope-intercept form is y = mx + c. An intercept is a point on the y-axis by which the slope of the line passes. The point where the line crosses the x-axis is known as the x-intercept and the point where the line crosses the y-axis is known as the y-intercept. The Problems on Slope and Y-intercept in coordinate geometry is a combination of different types of questions. Start practicing the problems on slope-intercept from this page and score good marks in the exams.

**Also Read:**

- Worksheet on Slope and Y-intercept

## Slope and Y-Intercept Form Problems with Solutions

**Example 1.**

Determine the slope and y-intercept of the line 6x – 5y + 7 = 0

**Solution:**

Given that the equation is 6x – 5y – 7 = 0

-5y = -6x + 7

y = −6/−5x + 7/−5.

y = 6/5x – 7/5.

Comparing this with y = mx + c, we have: m = 6/5 and c = -7/5

Therefore, slope = 6/5 and y-intercept = -7/5

**Example 2.**

What is the slope and y-intercept of the equation 2x – 3y + 4 = 0?

**Solution:**

Given that the equation is

2x – 3y + 4 = 0

3y = 2x + 4

y = 2/3x + 4/3.

y = 2/3x + 4/3

Comparing the equation with y = mx + c,

we have m = 2/3.

Therefore, the slope of the line is 4/3.

**Example 3.**

Find the slope and y-intercept of the equation √3x – 3y + 8 = 0

**Solution:**

Given that the equation is √3x – 3y + 8 = 0

3y = √3x + 8

y = √3/3x + 8/3

Comparing with the equation y = mx + c

Then we have m = √3/3 and c = 8/3

Therefore the slope = √3/3 and y-intercept = 8/3.

**Example 4.**

What is the slope and y-intercept of the equation 6x – 7y + 8 = 0?

**Solution:**

Given that the equation is

6x – 7y + 8 = 0

7y = 6x + 8

y = 6/7x + 8/7.

Comparing the equation with y = mx + c,

we have m = 6/7 and c = 8/7

Therefore, the slope of the line is 6/7 and y-intercept = 8/7.

**Example 5.**

What is the slope and y-intercept of the equation 9x – 10y -11 = 0?

**Solution:**

Given that the equation is

9x – 10y – 11 = 0

10y = 9x – 11

y = 9/10x – 11/10.

Comparing the equation with y = mx + c,

we have m = 9/10 and c = 11/10

Therefore, the slope of the line is 9/10 and y-intercept = 11/10

**Example 6.**

If the slope of the line joining the points A(x,2) and B(3,6) is 5/4, find the value of x.

**Solution:**

Given that the two points are

A(x,2) and B(3,6)

x_{1} = x, y_{1} = 2, x_{2} = 3, y_{2} = 6

Given slope = 5/4

We know that

x_{2} – x_{1}/y_{2} – y_{1}

3 – x/6 – 2 = 5/4

3 – x/4 = 5/4

12 – 4x = 20

12 – 20= 4x

-8 = 4x

x = -2

Hence the value of x = -2.

**Example 7.**

Find the slope of the line joining the points (4,8) and (5,2)

**Solution:**

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

Slope of the line = y_{2} – y_{1}/x_{2} – x_{1}

= 2-8/5 – 4

= -6/1

= -6/1

= -6

Therefore the slope of the given points are 6.

**Example 8.**

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

**Solution:**

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

x_{1} = 1, y_{1} = 2, x_{2} = 3 and y_{2} = 4

slope is (y_{2}-y_{1})/(x_{2}-x_{1})

(4 – 2)/(3 -1)

= 2/2

Slope =1

then y=mx+c

you get x-y+1=0

at y axis x=0

y = 1

Therefore y-intercept = 1

**Example 9.**

What is the slope and y-intercept of the equation x – y + 1 = 0?

**Solution:**

Given that the equation is

x – y + 1 = 0

y = x + 1

Comparing the equation with y = mx + c,

we have m = 1 and c = 1

Therefore, the slope of the line is 1, and y-intercept = 1.

**Example 10.**

What is the slope and y-intercept of the equation x – 3y – 7 = 0?

**Solution:**

Given that the equation is

x – 3y – 7 = 0

3y = x – 7

y = 1/3x – 7/3.

Comparing the equation with y = mx + c,

we have m = 1/3 and c = 7/3

Therefore, the slope of the line is 1/3 and y-intercept = 7/3.