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

$\sf\dashrightarrow \red{B(x_2,y_2)=(x,5)} \\ \\ </p><p></p><p>\sf\dashrightarrow \red{x_1=2} \\ \\ </p><p></p><p>\sf\dashrightarrow \red{x_2=x} \\ \\ </p><p></p><p>\sf\dashrightarrow \red{y_1=-7} \\ \\ </p><p></p><p>\sf\dashrightarrow \red{y_2= 5} \\ \\ </p><p></p><p>\large\underline\bold{\purple{\mathfrak{TO\:FIND,}}} \\ \\ </p><p></p><p>\sf\dashrightarrow \green{the\:value\:of\:x} \\ \\ </p><p></p><p></p><p>\rm{\boxed{\sf{ \circ\:\: slope= \dfrac{y_2-y_1}{x_2-x_1}\:\: \circ}}} \\ \\ </p><p></p><p>\large\underline\pink{\mathfrak{SOLUTION,}} \\ \\ </p><p></p><p>\sf\therefore\text{ \red{putting the values in the formula and solving it,}} \\ \\ </p><p></p><p>\sf\dashrightarrow \blue{\dfrac{5-(-7)}{x-2} = 3} \\ \\ </p><p></p><p>\sf\implies \blue{\dfrac{ 5+7}{x-2}= 3} \\ \\ </p><p></p><p>\sf\implies \blue{ \dfrac{ 12}{x-2}= 3} \\ \\ </p><p></p><p>\sf\implies \blue{ 12= 3 \times(x-2) } \\ \\ </p><p></p><p>\sf\implies \blue{12= 3x-6} \\ \\ </p><p></p><p>\sf\implies \blue{ 12+6=3x} \\ \\ </p><p></p><p>\sf\implies \blue{18= 3x}</p><p></p><p>\sf\implies \blue{x= \dfrac{ 18}{3}} \\ \\ </p><p></p><p>\sf\implies \blue{x=\cancel \dfrac{ 18}{3}} \\ \\ </p><p></p><p>\sf\implies \green{x=6} \\ \\ </p><p></p><p>\rm{\boxed{\sf{ \circ\:\: x= 6\:\: \circ}}} \\ \\ </p><p></p><p>\large\underline\mathtt{\purple{THE\:VALUE\:OF\:X\:IS\:6.}} \: </p><p></p><p> \:$