Find the slope and $y$-intercept of the graph of this linear equation.
$y=\frac{5}{7} x+9$
slope: $\square$ $y$-intercept: $\square$
Answer (1)
The equation is in slope-intercept form: y = m x + b .
Identify the slope m as the coefficient of x : m = 7 5 .
Identify the y -intercept b as the constant term: b = 9 .
The slope is 7 5 and the y -intercept is 9 .
Explanation
Understanding the Equation We are given the linear equation y = 7 5 x + 9 . Our goal is to identify the slope and y -intercept of this equation.
Recalling Slope-Intercept Form Recall the slope-intercept form of a linear equation: 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 = 7 5 x + 9 with the slope-intercept form y = m x + b , we can directly identify the slope and y -intercept.
Determining the Values The coefficient of x in the given equation is 7 5 , so the slope m = 7 5 . The constant term in the given equation is 9 , so the y -intercept b = 9 .
Final Answer Therefore, the slope of the line is 7 5 and the y -intercept is 9 .
Examples
Understanding slope and y-intercept is crucial in many real-world applications. For instance, if you're analyzing a graph that represents the cost of producing items, the slope could represent the cost per item, and the y-intercept could represent the fixed costs. Similarly, in physics, if you're looking at a velocity-time graph, the slope represents acceleration, and the y-intercept represents the initial velocity. These concepts are fundamental in interpreting and predicting trends in various fields.
