What is the slope? y = 2/3x + 7
Understand the Problem
The question is asking for the slope of the linear equation given in slope-intercept form (y = mx + b). Here, the slope is represented by the coefficient of x.
Answer
The slope is \( \frac{2}{3} \).
Answer for screen readers
The slope is ( \frac{2}{3} ).
Steps to Solve
- Identify the slope-intercept form
The slope-intercept form of a linear equation is given by:
$$ y = mx + b $$
where ( m ) is the slope and ( b ) is the y-intercept.
- Find the slope ( m )
In the equation provided,
$$ y = \frac{2}{3}x + 7 $$
the coefficient of ( x ) is ( \frac{2}{3} ). This means the slope ( m ) is ( \frac{2}{3} ).
- State the slope
The value of ( m ) represents the slope of the linear equation.
The slope is ( \frac{2}{3} ).
More Information
The slope represents the rate of change of ( y ) with respect to ( x ). In this case, for every increase of 3 units in ( x ), ( y ) increases by 2 units.
Tips
- Confusing the y-intercept with the slope. Remember that the slope is always the coefficient of ( x ).
- Misreading the fraction; ensure to simplify and understand fractions correctly.
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