Question

Find equation of line passing through the two points (3,5) and (-4,2)

Answer 1

Answer:

$\longrightarrow \displaystyle \Huge \boxed{\mathsf{Y=\frac{3}{7}x+\frac{26}{7}  }}}$

Step-by-step explanation:

SLOPE FORMULA:

$\Rightarrow \displaystyle \mathsf{\frac{Y_2-Y_1}{X_2-X_1} }$

SLOPE-INTERCEPT FORM:

$\Rightarrow \displaystyle \mathsf{y=mx+b}$

SOLUTIONS & SOLVE:

(3,5) and (-4,2)

y₂=2

y₁=5

x₂=(-4)

x₁=3

Solve.

$\displaystyle \mathsf{\frac{2-5}{(-4)-3}=\frac{-3}{-7}=\boxed{\mathsf{\frac{3}{7}}}}}   }$

So, the slope is 3/7.

m represents the slope.

b represents the y-intercept.

Y-intercept is 26/7.

y=3/7x+26/7

$\Rightarrow \Large\boxed{\mathsf{Y=\frac{3}{7}x+\frac{26}{7}  }}$

As a result, the correct answer is y=3/7x+26/7.

Answer 2

$\large \sf \underline{ \underline{ \: Answer : \: \: \: }}$

$\star \: \: \sf7y - 3x - 26 = 0$

$\large \sf \underline{ \underline{ \: Solution : \: \: \: }}$

We know that , the equation of the line passing through the points $\sf( x_{1}, y_{1})$ and $\sf(x _{2} ,y_{2})$ is given by

$\sf \large \underline{ \: \: \: \fbox{ (y - y_{1}) = \bigg(\frac{y_{2} - y_{1}}{x_{2} - x_{1}} \bigg) (x - x_{1}) \: \: } \: \: \: \: \: }$

So , the equation of line passing through points (3,5) and (-4,2) is

$\implies\sf (y - 5) = \bigg( \frac{2 - 5}{ (- 4) - 3} \bigg)(x - 3) \\ \\\implies\sf (y - 5) = \bigg(\frac{ \cancel{- }3}{ \cancel{ - } 7} \bigg )(x - 3) \\ \\\implies\sf 7(y - 5) = 3(x - 3) \\ \\ \implies\sf 7y - 3x - 26 = 0$

Hence , the required equation of line is $\sf7y - 3x - 26 = 0$