# Slope & *y*-intercept of a Line

Home | Online Math Tutoring | 8th Grade Math Tutoring | **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 ** m** and making an

*y***-intercept** of ** c **units is given by

**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.

+1-269-763-4602

+1-269-763-5024

#### Quick Links

#### Follow Us

#### Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘*Learning by Design*’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘*What do you want to learn today?*’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved