Find the coordinates of the points of intersection with the coordinate axes of the equation 5x-y + 2

Find the coordinates of the points of intersection with the coordinate axes of the equation 5x-y + 2 = 0 whether the point (-2; 3) belongs to the graph of the equation.

1) Point of intersection with the x-axis: y-coordinate = 0.

5x – y + 2 = 0.

5x – 0 + 2 = 0.

5x + 2 = 0.

5x = -2.

x = -2/5. The point of intersection with the x-axis (-2/5; 0).

2) Point of intersection with the y-axis: x-coordinate = 0.

5 * 0 – y + 2 = 0.

-y + 2 = 0.

-y = -2.

y = 2. The point of intersection with the y-axis (0; 2).

3) The coordinates of the point (-2; 3) are equal: x = -2; y = 3. Substitute the values of x and y into the equation of the line and check the equality.

5 * (-2) – 3 + 2 = 0.

-10 – 3 + 2 = 0.

-13 + 2 = 0.

-11 = 0 (wrong), the point does not belong to the graph of the function.