Question

the slope of line segment joining A(3, -2) B(x, 6) is 10 then find x,
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Answer 1

Answer:

x=3.8

Step-by-step explanation:

A=3,-2

B=x,6

slope of line = y2-y1/x2-x1

so,

6-(-2)/x-3=10

8=10(x-3)

8=10x-30

10x=8+30

10x=38

x=38/10

x=3.8

Answer 2

Given

Two points A(3,-2) & B (x,6)

slope of the two given points is 10

To Find

Value of x

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

When two points and a slope is given or we have to find slope we use slope formula which is :

$\sf\bold{ \: m = \dfrac{y_{1} - y_{2}}{x_{1} - x_{2}}(where \: x_{1} \: is \: not \: equal \: to \: x_{2}) }$

We have m =10

x₁ =3 ; x₂=x

y₁=-2 ; y₂=6

Now ,put values into formula

=>m = y₁-y₂/x₁ -x₂

=>10= -2-6/3-x

=>10(3-x)= -2-6

=>30-10x= -8

=>-10x= -8 -30

=> -10x= -38

=>10x = 38

=>x=38/10

=>x= 3.8

x=3.8

Therefore,the value of x is 3.8

Extra information=>

• if two slopes are equal then the lines must be parallel to each other.
• If a line makes an angle x in the positive direction of x-axis then ,the slope is given by m=tanx ,where x ≠ 90°.
• If two lines are perpendicular to each other then their product of their slopes equal to -1 .e.g., m₁ × m₂= -1