|
|
|
|
|
|
|
|
7. Find Slope, X-intercept, Y-intercept of a line example
( Enter your problem )
|
- Find the slope and y-intercept of the line 2x+3y=4
- Find x-intercept and y-intercept of the line 2x+3y=4
- Find the slope, x-intercept and y-intercept of the line 2x+3y=4
- Find the slope, x-intercept and y-intercept of the line joining the points A(1,3) and B(3,5)
|
Other related methods
- Distance, Slope of two points
- Points are Collinear or Triangle or Quadrilateral form
- Find Ratio of line joining AB and is divided by P
- Find Midpoint or Trisection points or equidistant points on X-Y axis
- Find Centroid, Circumcenter, Area of a triangle
- Find the equation of a line using slope, point, X-intercept, Y-intercept
- Find Slope, X-intercept, Y-intercept of a line
- Find the equation of a line passing through point of intersection of two lines and slope or a point
- Find the equation of a line passing through a point and parallel or perpendicular to Line-2 or point-2 and point-3
- Find the equation of a line passing through point of intersection of Line-1, Line-2 and parallel or perpendicular to Line-3
- For two lines, find Angle, intersection point and determine if parallel or perpendicular lines
- Reflection of points about x-axis, y-axis, origin
|
|
4. Find the slope, x-intercept and y-intercept of the line joining the points A(1,3) and B(3,5)
1. Find the slope, x-intercept and y-intercept of the line joining the points `A(1,3)` and `B(3,5)`
Solution:
The given points are `A(1,3),B(3,5)`
`:. x_1=1,y_1=3,x_2=3,y_2=5`
Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`:. (y-3)/(5-3)=(x-1)/(3-1)`
`:. (y-3)/(2)=(x-1)/(2)`
`:. (y-3)/(1)=(x-1)/(1)`
`:. (y-3)=(x-1)`
`:. y -3=x -1`
`:. x-y+2=0`
The given equation sholud be written in the form `y=mx+c`
`x-y+2=0`
`:. y=1x+2`
Comparing this equation with `y=mx+c`, we get
`m=1` and `c=2`
Now, to find the intercept on X-axis put `y=0` in the given equation.
The value of `x` will give the intercept of the line on X-axis
`:. x-y=-2`
`:. x-(0)=-2`
`:. x=-2`
Hence, the slope of the line is `1`, the x-intercept is `-2` and the y-intercept is `2`
2. Find the slope, x-intercept and y-intercept of the line joining the points `A(4,-8)` and `B(5,-2)`
Solution:
The given points are `A(4,-8),B(5,-2)`
`:. x_1=4,y_1=-8,x_2=5,y_2=-2`
Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`:. (y+8)/(-2+8)=(x-4)/(5-4)`
`:. (y+8)/(6)=(x-4)/(1)`
`:. (y+8)=6(x-4)`
`:. y +8=6x -24`
`:. 6x-y-32=0`
The given equation sholud be written in the form `y=mx+c`
`6x-y-32=0`
`:. y=6x-32`
Comparing this equation with `y=mx+c`, we get
`m=6` and `c=-32`
Now, to find the intercept on X-axis put `y=0` in the given equation.
The value of `x` will give the intercept of the line on X-axis
`:. 6x-y=32`
`:. 6x-(0)=32`
`:. 6x=32`
`:. x=16/3`
Hence, the slope of the line is `6`, the x-intercept is `16/3` and the y-intercept is `-32`
3. Find the slope, x-intercept and y-intercept of the line joining the points `A(7,1)` and `B(8,9)`
Solution:
The given points are `A(7,1),B(8,9)`
`:. x_1=7,y_1=1,x_2=8,y_2=9`
Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`:. (y-1)/(9-1)=(x-7)/(8-7)`
`:. (y-1)/(8)=(x-7)/(1)`
`:. (y-1)=8(x-7)`
`:. y -1=8x -56`
`:. 8x-y-55=0`
The given equation sholud be written in the form `y=mx+c`
`8x-y-55=0`
`:. y=8x-55`
Comparing this equation with `y=mx+c`, we get
`m=8` and `c=-55`
Now, to find the intercept on X-axis put `y=0` in the given equation.
The value of `x` will give the intercept of the line on X-axis
`:. 8x-y=55`
`:. 8x-(0)=55`
`:. 8x=55`
`:. x=55/8`
Hence, the slope of the line is `8`, the x-intercept is `55/8` and the y-intercept is `-55`
4. Find the slope, x-intercept and y-intercept of the line joining the points `A(4,8)` and `B(5,5)`
Solution:
The given points are `A(4,8),B(5,5)`
`:. x_1=4,y_1=8,x_2=5,y_2=5`
Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`:. (y-8)/(5-8)=(x-4)/(5-4)`
`:. (y-8)/(-3)=(x-4)/(1)`
`:. (y-8)=-3(x-4)`
`:. y -8=-3x +12`
`:. 3x+y-20=0`
The given equation sholud be written in the form `y=mx+c`
`3x+y-20=0`
`:. y=-3x+20`
Comparing this equation with `y=mx+c`, we get
`m=-3` and `c=20`
Now, to find the intercept on X-axis put `y=0` in the given equation.
The value of `x` will give the intercept of the line on X-axis
`:. 3x+y=20`
`:. 3x+(0)=20`
`:. 3x=20`
`:. x=20/3`
Hence, the slope of the line is `-3`, the x-intercept is `20/3` and the y-intercept is `20`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
|
|
|
Share this solution or page with your friends.
|
|
|
|
