4. If slope of the line joining points A(x,0), B(-3,-2) is 2/7, find the value of x
1. If slope of the line joining points `A(x,0), B(-3,-2)` is `2/7`, find the value of `x`
Solution:
Points are `(x,0),(-3,-2)` and Slope `=2/7`
`:. x_1=x,y_1=0,x_2=-3,y_2=-2,m=2/7`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. 2/7=(-2)/(-3-x)`
`:. 2/7*(-3-x)=-2`
`:. -3-x=-2*7/2`
`:. -3-x=-7`
`:. x=-3+7`
`:. x=4`
2. If slope of the line joining points `A(2,x), B(-3,7)` is `1`, find the value of `x`
Solution:
Points are `(2,x),(-3,7)` and Slope `=1`
`:. x_1=2,y_1=x,x_2=-3,y_2=7,m=1`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. 1=(7-x)/(-3-2)`
`:. 1=(7-x)/(-5)`
`:. 1*-5=7-x`
`:. -5=7-x`
`:. x=7+5`
`:. x=12`
3. If slope of the line joining points `A(x,5), B(-1,2)` is `3/4`, find the value of `x`
Solution:
Points are `(x,5),(-1,2)` and Slope `=3/4`
`:. x_1=x,y_1=5,x_2=-1,y_2=2,m=3/4`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. 3/4=(2-5)/(-1-x)`
`:. 3/4*(-1-x)=-3`
`:. -1-x=-3*4/3`
`:. -1-x=-4`
`:. x=-1+4`
`:. x=3`
4. If slope of the line joining points `A(2,5), B(x,3)` is `2`, find the value of `x`
Solution:
Points are `(2,5),(x,3)` and Slope `=2`
`:. x_1=2,y_1=5,x_2=x,y_2=3,m=2`
Slope `m = (y_2-y_1)/(x_2-x_1)`
`:. 2=(3-5)/(x-2)`
`:. 2=(-2)/(x-2)`
`:. 2*(x-2)=-2`
`:. x-2=-2/2`
`:. x=-1+2`
`:. x=1`
5. If slope of the line joining points `A(x,2), B(6,-8)` is `-5/4`, find the value of `x`
Solution:
Points are `(x,2),(6,-8)` and Slope `=-5/4`
`:. x_1=x,y_1=2,x_2=6,y_2=-8,m=-5/4`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. -5/4=(-8-2)/(6-x)`
`:. -5/4*(6-x)=-10`
`:. 6-x=-10*-4/5`
`:. 6-x=8`
`:. x=6-8`
`:. x=-2`
6. If slope of the line joining points `A(-2,x), B(5,-7)` is `-1`, find the value of `x`
Solution:
Points are `(-2,x),(5,-7)` and Slope `=-1`
`:. x_1=-2,y_1=x,x_2=5,y_2=-7,m=-1`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. -1=(-7-x)/(5+2)`
`:. -1=(-7-x)/(7)`
`:. -1*7=-7-x`
`:. -7=-7-x`
`:. x=-7+7`
`:. x=0`
7. If slope of the line joining points `A(2,3), B(x,6)` is `3/5`, find the value of `x`
Solution:
Points are `(2,3),(x,6)` and Slope `=3/5`
`:. x_1=2,y_1=3,x_2=x,y_2=6,m=3/5`
Slope `m = (y_2-y_1)/(x_2-x_1)`
`:. 3/5=(6-3)/(x-2)`
`:. 3/5=(3)/(x-2)`
`:. 3/5*(x-2)=3`
`:. x-2=3*5/3`
`:. x=5+2`
`:. x=7`
8. If slope of the line joining points `A(-3,4), B(5,x)` is `-5/4`, find the value of `x`
Solution:
Points are `(-3,4),(5,x)` and Slope `=-5/4`
`:. x_1=-3,y_1=4,x_2=5,y_2=x,m=-5/4`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. -5/4=(x-4)/(5+3)`
`:. -5/4=(x-4)/8`
`:. -5/4*8=x-4`
`:. x-4=-10`
`:. x=-10+4`
`:. x=-6`
9. If slope of the line joining points `A(0,x), B(5,-2)` is `-9/5`, find the value of `x`
Solution:
Points are `(0,x),(5,-2)` and Slope `=-9/5`
`:. x_1=0,y_1=x,x_2=5,y_2=-2,m=-9/5`
Slope `=m=(y_2-y_1)/(x_2-x_1)`
`:. -9/5=(-2-x)/(5)`
`:. -9/5*5=-2-x`
`:. -9=-2-x`
`:. x=-2+9`
`:. x=7`
This material is intended as a summary. Use your textbook for detail explanation.
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