Give the slope and the $y$-intercept of the line with the given equation. Then, graph the linear equation.
$y=3 x+7$
What is the slope? Select the correct choice below and fill in any answer boxes within your choice.
A. The slope is $\square$ .
(Simplify your answer.)
B. The slope is undefined.
Answer (2)
The equation is in slope-intercept form: y = m x + b .
Identify the slope m as the coefficient of x : m = 3 .
Identify the y -intercept b as the constant term: b = 7 .
The slope is 3 and the y -intercept is 7, so the answer is 3 .
Explanation
Analyze the equation The given equation is y = 3 x + 7 . We need to identify the slope and the y -intercept of this line.
Recall slope-intercept form The equation is already in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y -intercept.
Identify slope and y-intercept Comparing y = 3 x + 7 with y = m x + b , we can see that the coefficient of x is 3, so the slope m = 3 . The constant term is 7, so the y -intercept b = 7 .
State the results Therefore, the slope of the line is 3 and the y -intercept is 7.
Examples
Understanding the slope and y-intercept of a line is crucial in many real-world applications. For instance, imagine you are tracking the cost of a taxi ride. The initial fee (y-intercept) might be $5, and the cost per mile (slope) might be 2. S o , t h ee q u a t i o n re p rese n t in g t h e t o t a l cos tw o u l d b e y = 2x + 5 , w h ere x$ is the number of miles traveled. Knowing the slope and y-intercept helps you quickly calculate the total cost for any distance. Similarly, in business, understanding linear relationships can help predict revenue based on sales or costs based on production volume.
The slope of the line is 3, and the y-intercept is 7. Therefore, the answer to the selection is A. The slope is 3. This information helps in analyzing the linear relationship represented by the equation.
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