Write the equation of the line satisfying the given condition. Perpendicular to x = 4 and passing through the point (7, 2)

Prependicular to x = 4 means that the line will have a gradient of 0.

Passing through the point, (7,2) is handy, but all we need is the y co-ordinate.

The line is y = 2.

It satisfies the requirements.

To find the equation of a line perpendicular to the line x = 4 and passing through the point (7, 2), we can analyze the characteristics of the given line:

The equation x = 4 represents a vertical line. Since it is a vertical line, the slope of this line is undefined (as the denominator of the slope formula would be zero).

To find the slope of a line perpendicular to this vertical line, we can use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line would be the negative reciprocal of the slope of the vertical line.

Since the slope of the vertical line x = 4 is undefined, the slope of the perpendicular line would be 0.

Now that we know the slope (m = 0) and a point on the line (7, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) represents the coordinates of the given point, and m represents the slope.

Plugging in the values into the point-slope form, we get:

y - 2 = 0(x - 7)

Simplifying the equation, we have:

y - 2 = 0

Finally, we can rewrite the equation in slope-intercept form (y = mx + b), which is the standard form for linear equations:

y = 0

Therefore, the equation of the line perpendicular to x = 4 and passing through the point (7, 2) is y = 0.