Answer:
To graph the lines, we have:
- The line x=3 is a vertical line passing through x=3 on the x-axis.
- The line y = 5 is a horizontal line passing through y=5 on the y-axis.
Please note that the graph may not be visible in this text-based format, but you can plot the points (4,5) and observe that the line y = 5 is horizontal and passes through the point (4,5). The line x=3 is vertical and parallel to the y-axis.
Explanation:
To find the equation of a line that is perpendicular to the line x=3 and passes through the point (4,5), we need to determine the slope of the perpendicular line.
The line x=3 is a vertical line that is parallel to the y-axis. Since it is parallel to the y-axis, the slope of this line is undefined.
A line that is perpendicular to a vertical line has a slope of 0. Therefore, the slope of the perpendicular line we are looking for is 0.
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - y1 = m(x - x1)
Substituting the values of the point (4,5) and the slope 0 into the equation, we get:
y - 5 = 0(x - 4)
Simplifying the equation:
y - 5 = 0
To express the equation in slope-intercept form (y = mx + b), we can rewrite it as:
y = 5
The equation of the line that is perpendicular to x=3 and passes through the point (4,5) is y = 5.
To graph the lines, we have:
- The line x=3 is a vertical line passing through x=3 on the x-axis.
- The line y = 5 is a horizontal line passing through y=5 on the y-axis.
Please note that the graph may not be visible in this text-based format, but you can plot the points (4,5) and observe that the line y = 5 is horizontal and passes through the point (4,5). The line x=3 is vertical and parallel to the y-axis.