Question

Find the equation of a straight line passing through (-8,4) and making equal intercepts on the coordinate axes

Answer 1

EXPLANATION.

Equation of a straight lines passing through (-8,4).

making equal intercept on the co-ordinate axis.

As we know that,

Let we assume that x-intercept & y-intercept = t

equation of line,

⇒ x/a + y/b = 1.

We can write as,

⇒ x/t + y/t = 1.

⇒ -8/t + 4/t = 1.

⇒ -8 + 4 = t.

⇒ -4 = t.

Put the value of t = -4 in equation, we get.

⇒ x/-4 + y/-4 = 1.

⇒ x + y = -4.

⇒ x + y + 4 = 0.

                                                                                         

MORE INFORMATION.

Equation of straight lines parallel to axes.

(1) = Equation of x-axis ⇒ y = 0.

(2) = Equation of a line parallel to x-axes at a distance of b ⇒ y = b.

(3) = Equation of y-axis ⇒ x = 0.

(4) = Equation of a line parallel to y-axes and at a distance of a ⇒ x = a.

Answer 2

$\\ \rm \large \underline{ \: Question :- }$

Find the equation of a straight line passing through (-8,4) and making equal intercepts on the coordinate axes

$\\ \rm \large \underline{ \: Answer :- }$

Let x - intercept and y intercept "a" , the equation of line is

$\\ \\ \mathsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \frac{x}{a} + \frac{y}{a} = 1}$

$\\ \tt \: The \: line \: passed \: through \: the \: point \: (-8,4)$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \: \: \: \frac{( - 8)}{a} + \frac{4}{a} \: = \: 1$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \: \: \: \frac{( - 8 + 4)}{a} \: = \: 1$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \: \: \: \frac{( - 4)}{a} \: = \: 1$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \: \: \underline{\boxed{ \orange{\frak{ \: a \: = \: ( - 4)}}}}$

$\\ \tt \: Therefore, \: The \: equation \: of \: line \: is \:$

$\\ \\ \mathsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \frac{x}{ - 4} + \frac{y}{ - 4} = 1}$

$\\ \tt \: \: \: \: \: \: Now, \: multiple \: whole \: equation \: by \: (-4)$

$\\ \\ \mathsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: {x} + {y} = { - 4} }$

$\\ \\ \mathsf{\: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \underline { \boxed{ \orange { \frak{ \: {x} + {y} + 4 = 0}}}} }$

$\\ \\ \: \: \: \: \: \: \: † \underline{ \: \bf \: The \: equation \: of \: line \: is \: x \: + \: y \: + \: 4 \: = \: 0 \: \: }$