Question

if slope of the line through [2, -7] and [x, 5] is 3 then x =​

Answer 1

$\huge\mathtt{\fbox{\red{Answer✍︎}}}$

$\large\underline\pink{\mathfrak{GIVEN,}}$

$\sf\dashrightarrow \red{A(x_1,y_1)=(2,-7)}$

$\sf\dashrightarrow \red{B(x_2,y_2)=(x,5)}$

$\sf\dashrightarrow \red{x_1=2}$

$\sf\dashrightarrow \red{x_2=x}$

$\sf\dashrightarrow \red{y_1=-7}$

$\sf\dashrightarrow \red{y_2= 5}$

$\large\underline\bold{\purple{\mathfrak{TO\:FIND,}}}$

$\sf\dashrightarrow \green{the\:value\:of\:x}$

FORMULA ,

$\rm{\boxed{\sf{ \circ\:\: slope= \dfrac{y_2-y_1}{x_2-x_1}\:\: \circ}}}$

$\large\underline\pink{\mathfrak{SOLUTION,}}$

$\sf\therefore\text{ \red{putting the values in the formula and solving it,}}$

$\sf\dashrightarrow \blue{\dfrac{5-(-7)}{x-2} = 3}$

$\sf\implies \blue{\dfrac{ 5+7}{x-2}= 3}$

$\sf\implies \blue{ \dfrac{ 12}{x-2}= 3}$

$\sf\implies \blue{ 12= 3 \times(x-2) }$

$\sf\implies \blue{12= 3x-6}$

$\sf\implies \blue{ 12+6=3x}$

$\sf\implies \blue{18= 3x}$

$\sf\implies \blue{x= \dfrac{ 18}{3}}$

$\sf\implies \blue{x=\cancel \dfrac{ 18}{3}}$

$\sf\implies \green{x=6}$

$\rm{\boxed{\sf{ \circ\:\: x= 6\:\: \circ}}}$

$\large\underline\mathtt{\purple{THE\:VALUE\:OF\:X\:IS\:6.}}$

Answer 2

Question:-

➡ If the slope of the line through (2, -7) and (x, 5) is 3 then find x.

Solution:-

Given,

$\sf x_{1} = 2$

$\sf x_{2} = x$

And,

$\sf y_{1} = - 7$

$\sf y_{2} = 5$

Now,

$\sf slope = \frac{ y_{2} - y_{1}}{ x_{2} - x_{1} }$

$\sf \implies \frac{ y_{2} - y_{1}}{ x_{2} - x_{1} } = 3$

$\sf \implies \frac{5 - ( - 7)}{x - 2} = 3$

$\sf \implies \frac{12}{x - 2} = 3$

$\sf \implies \frac{12}{3} = x - 2$

$\sf \implies 4 = x - 2$

$\sf \implies x = 4 + 2$

$\sf \implies x = 6$

Hence, the value of x is 6.

Answer:-

➡ The value of x is 6.