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masya89 [10]
3 years ago
6

What is the equation of a line parallel to the x-axis that passes though the point (4,5)? What is the slope of this line

Mathematics
1 answer:
Svetlanka [38]3 years ago
6 0

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)

<h3><u>Solution:</u></h3>

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

<h3><u>Method 2:</u></h3>

We know slope "m" = 0

Given point is (4, 5)

<em><u>The slope intercept form is given as:</u></em>

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)

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<h3><u>Solution</u>:-</h3>

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\green{ \underline { \boxed{ \sf{y=mx+c}}}}

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