What is the slope, m, of the graph of this line? What is the y-intercept of the graph of this line? Enter your answer as an ordered pair in the form (x, y).
Understand the Problem
The question is asking for two things regarding a linear equation: the slope of the graph of the line, and the y-intercept, specifically to present the y-intercept as an ordered pair (x, y).
Answer
The slope is $m = -\frac{1}{4}$ and the y-intercept is $(0, -11)$.
Answer for screen readers
The slope of the graph of the line is $m = -\frac{1}{4}$.
The y-intercept of the graph as an ordered pair is $(0, -11)$.
Steps to Solve
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Identifying the slope To find the slope of the line given by the equation ( y = -\frac{1}{4}x - 11 ), we identify the coefficient of ( x ). In this case, the slope ( m ) is given directly as ( m = -\frac{1}{4} ).
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Finding the y-intercept The y-intercept is the value of ( y ) when ( x = 0 ). We can substitute ( x = 0 ) into the equation: $$ y = -\frac{1}{4}(0) - 11 = -11 $$ Thus, the y-intercept is ( (0, -11) ).
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Presenting the y-intercept as an ordered pair We express the y-intercept found in the previous step as an ordered pair: $$ \text{Ordered pair: } (0, -11) $$
The slope of the graph of the line is $m = -\frac{1}{4}$.
The y-intercept of the graph as an ordered pair is $(0, -11)$.
More Information
The slope of a linear equation indicates how steep the line is and the direction it goes (negative in this case means it goes downwards). The y-intercept is where the line crosses the y-axis.
Tips
- Misreading the slope coefficient by forgetting to apply the negative sign.
- Confusing the y-intercept with other points on the graph, such as the x-intercept.
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