Question

Write an equation in slope-intercept form for the line that passes through (9, 12) and is perpendicular to y=4

Answer 1

The line perpendicular to y=4 and passing through (9, 12) is a vertical line. It cannot be expressed in traditional slope-intercept form but as x=9, which indicates its intersection with the x-axis.

Step-by-step explanation:

To write an equation in slope-intercept form for the line that passes through the point (9, 12) and is perpendicular to the line defined by y=4, we first need to understand the characteristics of the given line and what being perpendicular means.

The line y=4 is a horizontal line with a slope of 0 because it does not rise or fall as it moves along the x-axis. Perpendicular lines have slopes that are the negative reciprocals of each other. Since the slope of the given line is 0, the negative reciprocal of 0 is undefined. This means that a line perpendicular to y=4 will be vertical and cannot be expressed with a traditional slope-intercept form, y = mx + b.

However, a vertical line that passes through the point (9, 12) only crosses the x-axis at x=9. The equation for a vertical line is given by x = a, where a is the x-intercept. Hence, the equation for the line we are seeking is x = 9.

Answer 2


`x=9`

Step-by-step explanation:

First, let's determine the slope! We know that the line is perpendicular to
`y=4`. This line is just a horizontal line that crosses the y-axis with a slope of 0. The line perpendicular to this will have the form
`x=?`. This is a straight, vertical line with indeterminate slope.

The line passes through the point (9, 12). If the line is going straight up and down, it will intercept every y-value, but only one x-value. The x-value in this ordered pair is 9. Therefore, the equation of the line is
`x=9`.