write a linear equation in slope -intercept form of the line that passes through the point (3,0) and is perpendicular to y=4

The equation y=4 represents a horizontal line, since it has a constant value of y and the slope is zero. To find the equation of a line perpendicular to this, we need a slope that is the negative reciprocal of 0, which is undefined. This means the slope of the perpendicular line is 0. The line that passes through the point (3,0) and has a slope of 0 can be written in slope-intercept form as: y = mx + b where m is the slope and b is the y-intercept. Since the slope is 0, the equation becomes: y = 0x + b or simply: y = b To find the value of b, we can use the fact that the line passes through the point (3,0). Substituting this into the equation, we get: 0 = b Therefore, the equation of the line that passes through the point (3,0) and is perpendicular to y=4 is: y = 0 which is simply the x-axis.