A line with a slope of 1/6 passes through the points (0, 3) and (a, 4). What is the value of a?
Understand the Problem
The question is asking for the value of 'a' in a line that has a specific slope and passes through given points. The slope formula and the coordinates of the points will be used to solve for 'a'.
Answer
$$ a = 6 $$
Answer for screen readers
$$ a = 6 $$
Steps to Solve
- Identify the known variables
We know that one point is ( (0, 3) ) and the other point is ( (a, 4) ). The slope of the line is given as ( \frac{1}{6} ).
- Use the slope formula
The slope formula is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Where ( m ) is the slope, ( (x_1, y_1) = (0, 3) ), and ( (x_2, y_2) = (a, 4) ).
- Plug in the values into the slope formula
Now substituting the known values into the slope formula: $$ \frac{1}{6} = \frac{4 - 3}{a - 0} $$
- Simplify the equation
This simplifies to: $$ \frac{1}{6} = \frac{1}{a} $$
- Cross-multiply to solve for ( a )
Cross-multiply to get: $$ 1 \cdot a = 1 \cdot 6 $$
- Solve for ( a )
Therefore, we find: $$ a = 6 $$
$$ a = 6 $$
More Information
This result indicates that when the line passes through the points ( (0, 3) ) and ( (6, 4) ), and has a slope of ( \frac{1}{6} ), the value of ( a ) is 6.
Tips
- Forgetting to simplify the slope equation: Ensure to simplify fractions correctly before solving for ( a ).
- Not cross-multiplying properly: This step is crucial in equations that involve fractions; ensure to maintain equality.
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