What is the slope of the line given by the equation below?
y-9=15(x-5)
Answer (1)
Recognize the equation is in point-slope form: y − y 1 = m ( x − x 1 ) .
Compare the given equation y − 9 = 15 ( x − 5 ) with the point-slope form.
Identify the slope m as the coefficient of ( x − 5 ) .
The slope of the line is 15 .
Explanation
Understanding the Problem The equation of the line is given as y − 9 = 15 ( x − 5 ) . We need to find the slope of this line.
Recognizing Point-Slope Form The given equation is in point-slope form, which is y − y 1 = m ( x − x 1 ) , where m represents the slope of the line and ( x 1 , y 1 ) is a point on the line.
Identifying the Slope Comparing the given equation y − 9 = 15 ( x − 5 ) with the point-slope form y − y 1 = m ( x − x 1 ) , we can identify the slope m . In this case, m = 15 .
Final Answer Therefore, the slope of the line is 15.
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, in construction, the slope of a ramp determines its steepness, which affects its usability. In economics, the slope of a supply or demand curve indicates how sensitive the quantity supplied or demanded is to changes in price. In physics, the slope of a velocity-time graph represents acceleration. Knowing how to find the slope from an equation helps in analyzing and predicting these relationships.
