# 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.

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