Select the correct slope and $y$-intercept for the following linear equation: $y=-2 x+4$
Answer (2)
The equation is in slope-intercept form: y = m x + b .
Identify the slope m as the coefficient of x : m = − 2 .
Identify the y-intercept b as the constant term: b = 4 .
The slope is − 2 and the y-intercept is 4 : \boxed{{\text{slope} = -2, \ y\[\]\text{intercept} = 4}} .
Explanation
Understanding the Equation We are given the linear equation y = − 2 x + 4 and asked to identify its slope and y -intercept. This equation is already in slope-intercept form, which makes it easy to read off the values we need.
Recalling Slope-Intercept Form The slope-intercept form of a linear equation is y = m x + b , where m represents the slope and b represents the y -intercept.
Identifying Slope and Y-Intercept Comparing the given equation y = − 2 x + 4 to the slope-intercept form y = m x + b , we can see that the coefficient of x is − 2 , so the slope m = − 2 . The constant term is 4 , so the y -intercept b = 4 .
Stating the Answer Therefore, the slope of the given equation is − 2 and the y -intercept is 4 .
Examples
Understanding slope and y-intercept is crucial in many real-world applications. For example, if you are analyzing the cost of a taxi ride, the slope might represent the cost per mile, and the y-intercept could be the initial fee. Similarly, in physics, if you are studying the motion of an object, the slope of a distance-time graph represents the object's velocity, and the y-intercept represents the initial position. Linear equations are fundamental tools for modeling and understanding relationships between variables in various fields.
The slope of the equation y = − 2 x + 4 is − 2 and the y-intercept is 4 . Therefore, the values can be summarized as slope = − 2 and y-intercept = 4 .
;
