What is the slope of the line whose equation is $y-4=\frac{5}{2}(x-2)$?
Answer (2)
Recognize that the given equation is in point-slope form: y − y 1 = m ( x − x 1 ) .
Identify the slope m by comparing the given equation with the point-slope form.
Conclude that the slope of the line is 2 5 .
Explanation
Understanding the Problem The equation of the line is given as y − 4 = 2 5 ( x − 2 ) . 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 − 4 = 2 5 ( x − 2 ) with the point-slope form y − y 1 = m ( x − x 1 ) , we can directly identify the slope m . In this case, m = 2 5 .
Final Answer Therefore, the slope of the line is 2 5 .
Examples
Understanding the slope of a line is crucial in many real-world applications. For instance, in construction, the slope of a ramp determines its steepness, affecting accessibility. 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 and interpret the slope helps in making informed decisions and predictions in these and many other fields.
The slope of the line given by the equation y − 4 = 2 5 ( x − 2 ) is 2 5 . This slope can be identified directly from the equation since it is in point-slope form. The identified slope indicates how steep the line is.
;
