Slope of a line parallel to the x -axis is 0
y = 5 is the required equation of a line parallel to the x-axis that passes though the point (4,5)
Solution:
Given that a line parallel to the x-axis that passes though the point (4,5)
To find: slope of this line and equation of a line
The x -axis is a horizontal line with the equation y = 0 There are an infinite number of lines that are parallel to the x -axis, y = 0
All horizontal lines have slope of 0
If lines are parallel then they have the same slope. The slope of a line parallel to the x -axis is 0
The equation of a straight line parallel to x-axis at a distance b from it is y = b
Here "b" is the y - co-ordinate value
Here given point is (4, 5) so b = 5
The required equation is y = 5
Method 2:
We know slope "m" = 0
Given point is (4, 5)
The slope intercept form is given as:
y = mx + b --- eqn 1
Where "m" is the slope of line and "b" is the y - intercept
Substituting m = 0 and (x, y) = (4, 5)
5 = 0(4) + b
b = 5
Substitute b = 5 and m = 0 in eqn 1
y = 0 + 5
y = 5 is the required equation of a line parallel to the x-axis that passes though the point (4,5)