Question

at what point the graph of the linear equation 3 x + 5 y equal to 15 cuts the x-axis and y-axis​

Answer 1

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

Given equation of line is

$\rm :\longmapsto\:3x + 5y = 15$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:3(0) + 5y = 15$

$\rm :\longmapsto\:0 + 5y = 15$

$\rm :\longmapsto\:5y = 15$

$\rm :\longmapsto\:y = 3$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:3x + 5(0) = 15$

$\rm :\longmapsto\:3x + 0 = 15$

$\rm :\longmapsto\:3x = 15$

$\rm :\longmapsto\:x = 5$

Substituting 'x = 3' in the given equation, we get

$\rm :\longmapsto\:3(3) + 5y = 15$

$\rm :\longmapsto \: 9 + 5y = 15$

$\rm :\longmapsto \: 5y = 15 - 9$

$\rm :\longmapsto \: 5y = 6$

$\rm :\longmapsto\:y = 1.2$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 5 & \sf 0 \\ \\ \sf 3 & \sf 1.2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 3), (3 , 1. 2) & (5 , 0)

➢ See the attachment graph.

So,

Line intersects x - axis at (5, 0)

Line intersects y - axis at (0, 3)