Find the slope and $y$-intercept of the graph of the linear equation.
$y=-5 x+4$
Answer (1)
The equation is in slope-intercept form: y = m x + b .
Identify the slope m as the coefficient of x : m = − 5 .
Identify the y -intercept b as the constant term: b = 4 .
The slope is − 5 and the y -intercept is 4 .
Explanation
Understanding the Equation We are given the linear equation y = − 5 x + 4 . Our goal is to identify the slope and y -intercept of this equation.
Slope-Intercept Form Recall that the slope-intercept form of a linear equation is given by y = m x + b , where m represents the slope of the line and b represents the y -intercept (the point where the line crosses the y -axis).
Identifying Slope and y-intercept Comparing the given equation y = − 5 x + 4 with the slope-intercept form y = m x + b , we can directly identify the values of m and b .
Determining the Values The coefficient of x in the given equation is − 5 , so the slope m = − 5 . The constant term in the given equation is 4 , so the y -intercept b = 4 .
Final Answer Therefore, the slope of the line is − 5 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, the slope of a velocity-time graph represents acceleration, and the y-intercept represents the initial velocity. Recognizing these concepts helps in making informed decisions and predictions in various fields.
