Equate the straight line passing through the point M (8; 5) and intersecting the x-axis at a point 4

Equate the straight line passing through the point M (8; 5) and intersecting the x-axis at a point 4 units from the origin.

Let’s make the equation of the straight line, according to the condition of the problem.

We start by recalling the general form of the equation of the straight line: y = kx + b.

Since on the OX axis, there are two points that are 4 units away from the coordinate axis: (-4; 0) and (4; 0), we will consider two possible cases.

First case. Let’s compose a system of equations.

System of equations:

0 = -4k + m;

5 = 8k + m.

Let’s apply the addition method and subtract the first from the second equation.

5 = 12k;

k = 5/12.

Hence, m = 5/4.

Straight line equation:

y = 5 / 12x + 5/4.

Second case.

System:

0 = 4k + m;

5 = 8k + m.

System:

k = 5/4,

m = -5.

Equation y = 5/4 * x – 5.