Question

Find the length of intercepts on axes made by the line 5x + 3y – 15 = 0​

Answer 1

EXPLANATION.

Length of intercepts on axis made by the line,

⇒ 5x + 3y - 15 = 0.

In this question, we can solve by two methods,

Method = 1.

Let the equation,

⇒ 5x + 3y - 15 = 0 is written as,

⇒ 5x + 3y = 15.

⇒ 5x/15 + 3y/15 = 1.

⇒ x/3 + y/5 = 1.

As we know that,

Intercept Form = x/a + y/b = 1.

As we can see that,

x intercept = a = 3

y intercept = b = 5.

Method = 2.

Lets us considered the equation,

⇒ 5x + 3y - 15 = 0.

Put the equations in graph, we get.

Put the value of x = 0 in equation, we get.

⇒ 5(0) + 3y - 15 = 0.

⇒ 3y - 15 = 0.

⇒ 3y = 15.

⇒ y = 5.

Their Co-ordinates = (0,5).

Put the value of y = 0 in equation, we get.

⇒ 5x + 3(0) - 15 = 0.

⇒ 5x - 15 = 0.

⇒ x = 3.

Their Co-ordinates = (3,0).

If we can see the graph, we can see.

x intercept = a = 3.

y intercept = b = 5.

Answer 2

Given Question :-

• Find the length of intercepts on axes made by the line 5x + 3y – 15 = 0

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$\huge \orange{AηsωeR} ✍$

☆ Given :-

• The equation of line is 5x + 3y - 15 = 0.

☆To Find :-

• Length of intercept on axes.

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☆ Concept and Definition :-

Intercept form of a line

Consider a line L that makes x-intercept and y-intercept b on the axes. So that, L meets x-axis at the point (a, 0) and y-axis at the point (0, b). Thus, the equation of the line having the intercepts a and b on x-and y-axis respectively is given by

$\bf \:  ⟼ \dfrac{x}{a}+\dfrac{y}{b}=1$

Intercept on y - axis

• In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Intercept on x - axis

• In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a x-intercept or horizontal intercept is a point where the graph of a function or relation intersects the x-axis of the coordinate system. As such, these points satisfy y = 0.

How to Find X and Y Intercepts?

Consider a straight line equation Ax + By = C.

• To find the x-intercept, substitute y = 0 and solve for x.
• To find the y-intercept, substitute x =0 and solve for y.

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☆ Solution :-

$\bf \:The \: equation \: is \: 5x + 3y - 15 = 0 \: \sf \: ⟼(1)</p><p>$

$\bf \:To \: Find \: x - intercept, \: put \: y = 0 \: in \: eq \: (1)$

☆ we get

$\bf \:  ⟼ 5x + 3 \times 0 - 15 = 0$

$\bf \:  ⟼ 5x = 15$

$\bf\implies \:x = 3$

$\bf \:Hence, \: intercept \: on \: x- axis = 3 \: units$

$\begin{gathered}\bf\red{Now,}\end{gathered}$

$\bf \:To \: Find \: y - intercept, \: put \: x \: = 0 \: in \: eq \: (1)$

☆ we get

$\bf \:  ⟼ 5 \times 0 + 3y - 15 = 0$

$\bf \:  ⟼ 3y = 15$

$\bf \:  ⟼ y = 5$

$\bf \:Hence, \: intercept \: on \: y - axis = 5 \: units$

$\begin{gathered}\begin{gathered}\bf So = \begin{cases} &\bf{Intercept \: on \: x- axis = 3 \: units} \\ &\bf{Intercept \: on \: y axis = 5 \: units} \end{cases}\end{gathered}\end{gathered}$