Question

Question was provided via image upload.

Explanation:

Verify the given point on the line

Using the Linear Equation Graphing knowledge point

$$
LATEXBLOCK0
$$

Determine the condition for intersection

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Formulate a representative intersecting line

We choose a simple slope \(m = -1\) to find a clear intersecting equation.

$$
LATEXBLOCK2
$$

Answer:

Any equation of a line that passes through the point \((4, 6)\) and has a slope other than \(\frac{1}{2}\) will intersect the given line at \((4, 6)\).

A standard example of such an equation is:

$$y = -x + 10$$