# Slope & *y*-intercept of a Line

**Slope & y-intercept of a Line**

Since, we have already discussed the slope intercept form of the equation of a line; we will now learn how to find the **slope **& ** y-intercept** for any given equation of line.

Recall that, the length of the intercept made by of a line on the *Y-*axis is called* its y*

**-intercept**

*&*using

**Slope Intercept form**the equation of a line with

**slope**or gradient

**and making an**

*m*

*y***-intercept**of

**units is given by**

*c*

**y = mx + c.**

If the equation of the given line is *a x + by + d = 0.*

We rewrite the given equation in the slope intercept form by taking the term containing, *x* & constant, *d* on the other side of the equation i.e.* by = – a x – d or y = – d or y = +*

& then compare this with **y = mx + c** *we have slope m = & y intercept c=*

## Let us take a few examples

*Example:*

- Find the slope & y-intercept of the line x+y=7.Here, we can rewrite the equation as
*y = – x*+ 7*=*(-1)*x*+ 7.Hence here**slope**= (-1) &*m*,*y*-intercept*c*= 7. - Find the slope &
*y*-intercept of the line 4*x*+ 2*y =*8.Here, we can rewrite the equation as 2*y = –*4*x*+ 8*=*(-4)*x*+ 8.or*y =*(-2)*x*+ 4.Hence here**slope**= (-2) &*m*,*y*-intercept*c*= 4. - Find the slope &
*y*-intercept of the line 7*x*+ 8*y*– 15 = 0.Here, we can rewrite the equation as 8*y = –*7*x*+ 15*=*(-7)*x*+ (15). y= & y-intercept, c = .Hence here**slope**= & y-intercept, c= .*m* - Here, we can rewrite the equation as
*y =*(0)*x*+ 0.Hence here**slope,**= 0 &*m*,*y*-intercept*c*= 0.Find the slope &*y*-intercept of the line*y =*0.

### CHECK POINT

- Find the slope & y intercept of the line
*x*+*y –*75 = 8. - Find the slope & y intercept of the line 3
*x*– 7*y*+ 105*=0.* - Find the slope & y intercept of the line 10
*x*+ 2*y =26.* - Find the slope & y intercept of the line 15
*x*– 3*y*+ 75 = 0. - Find the slope & y intercept of the line 24
*x*+ 8*y =96.*

##### Answer key

- Slope
*m*= (-1),*y*-intercept = 83. - Slope
*m = ,*y-intercept =15. - Slope
*m =*(-5), y-intercept =13. - Slope
*m*= 5, y-intercept =25. - Slope
*m*= (-3),*y*-intercept = 12.

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

Tutoring

Test Prep

Worksheets

Pricing

About Us

Blog

Free Trial

Login

Terms of service

Privacy Policy

Money Back Guarantee

Technical requirements

FAQs

Job Opportunities

Sitemap

**Connect with us**

+1-269-763-4602

+1-269-763-5024

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

**Quick links**

Free Worksheets

Fact sheet

Sales Partner Opportunities

Parents

Passive Fundraising

Virtual Fundraising

Our Expert Tutors

Safe and Secure Tutoring

Interactive Online Tutoring

After School Tutoring

Elementary School Tutoring

Middle School Tutoring

High School Tutoring

Home Work Help

Math Tutors New York City

Press

©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2022 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird