Question

Determine the point on the graph of the equation 3x + 5y = 25 whose x-coordinate is 5

3

times its ordinate.

Also, find the points where the given line cuts the x-axis and y-axis.​

Answer 1

$Given \: equation \: of \: a \: straight \:line : \\3x+5y = 25$

$i) put \: x = 0 \:in \: the \: equation , we \:get$

$\implies 3 \times 0 + 5y = 25$

$\implies 5y = 25$

$\implies y = \frac{25}{5}$

$\implies y = 5$

$\implies A= (0,5)$

$ii) put \: x = 5 \:in \: the \: equation , we \:get$

$\implies 3 \times 5 + 5y = 25$

$\implies 15+ 5y = 25$

$\implies 5y = 25 - 15$

$\implies 5y = 10$

$\implies y = \frac{10}{5}$

$\implies y = 2$

$\implies B = (5,2)$

$Plotting \: the \: points \: A \: and \: B \:and \\joining \:them , we \: get \: a \: line$

$The \: line \: intersects \: Y- axis \: at \: ( 0,5)$

$Putc\: y= 0\: in \:the \: equation \: we \:get \\</p><p>X- intercept$

$\implies 3x + 5 \times 0 = 25$

$\implies 3x = 25$

$\implies x = \frac{25}{3}$

Therefore.,

$The \: line \: intersects \: X - axis \: at \\\Big( \frac{25}{3} , 0 \Big)$

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