Find the points of intersection of the graph of the equation with the coordinates

Find the points of intersection of the graph of the equation with the coordinates of the axes without plotting the graph: 2x-6y = 10

1. Find the points of intersection of the graph with the coordinate axes

2x – 6y = 10

Let us express the variable y in terms of the variable x.

– 6y = 10 – 2x;

y = – (10 – 2x) / 6;

y = – 2 * (5 – 2x) / 6;

y = (2x – 5) / 3.

If the graph intersects with the OY axis, then x = 0, substitute the x value into the equation

y = (2x – 5) / 3,

y = (2 * 0 – 5) / 3

y = – 5/3;

y = – 1.7, the point of intersection with the OY axis has coordinates (0; -1.7).

If the graph intersects with the OX axis, then y = 0, we substitute the value of y into the equation

y = (2x – 5) / 3

(2x – 5) / 3 = 0.

2x -5 = 0;

2x = 5;

x = 2.5, the point of intersection with the OX axis has coordinates (2.5; 0).