What is the slope of the line that passes through the points (5, 0) and has an x-intercept of 10?

Understand the Problem

The question is asking to calculate the slope of a line that goes through a specific point and has a defined x-intercept. To find the slope, we will use the formula for slope, which requires two points: (5, 0) and the x-intercept point (10, 0).

Answer

The slope of the line is $ m = 0 $.

Steps to Solve

Identify the Points We have the points ( (5, 0) ) (which is a given point on the line) and ( (10, 0) ) (which is the x-intercept).
Use the Slope Formula The slope ( m ) is calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ where ( (x_1, y_1) ) and ( (x_2, y_2) ) are the coordinates of the two points.
Substitute the Points into the Formula Substituting the points ( (5, 0) ) and ( (10, 0) ):

Let ( (x_1, y_1) = (5, 0) )
Let ( (x_2, y_2) = (10, 0) )

Now, substituting these values into the formula: $$ m = \frac{0 - 0}{10 - 5} $$

Calculate the Slope Now we simplify the expression: $$ m = \frac{0}{5} = 0 $$

The slope of the line is ( m = 0 ).

More Information

A slope of 0 means that the line is horizontal. This indicates that the y-value does not change as the x-value changes, which is consistent with the line passing through the x-axis.

Tips

Forgetting to use the correct formula for slope.
Mixing up the coordinates, which can lead to incorrect calculations.

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