Question

find the values of x,if the slope of the line joining the points (2,5) and (x,3) is 2​

Answer 1

Given:-

• (2,5) and (x,3)
• distance between these points is 2

To find:-

• value of x

Solution:-

〘 Distance formula -√(x2-x1)²+ (Y2-Y1)²〙

Put value

↦√(x2-x1)² +(Y2-Y1)²

↦√(x-2)²+(3-5)²=2

↦√(x-2)²+(3-5)²=2

↦Squaring both side

↦(x-2)²+(3-5)²=4

(a-b)²=a²+2ab+b²

↦x²+4-4x+4=4

↦x²+4-4x=0

↦x²-4x+4=0

↦x²-2x-2x+4=0

↦x(x-2)-2(x-2)=0

↦(x-2)(x-2)=0

↦x-2=0

↦x=2

$\huge\mathfrak{\purple{❝value\:of\:x\:is\:2❞}}$

Thanks

hope its helpful

Answer 2

Answer:

Slope of the line

$\frac{y2 - y1}{x2 - x1 } = 2\\ = \frac{3 - 5}{x - 2} = 2 \\ 3 - 5 = 2(x - 2) \\ - 2 = 2x - 4 \\ 2x = - 4 + 2 \\ 2x = - 2 \\ x = \frac{ - 2}{2 } \\ => x = - 1$