Give the slope and $y$-intercept of the line whose equation is given. Then graph the linear function.
$y=-3 x+1$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is $\square$ .
(Simplify your answer Type an integer or a fraction.)
B. The slope is undefined.
Answer (2)
The equation is in slope-intercept form: y = m x + b .
Identify the slope m = − 3 .
Identify the y-intercept b = 1 .
The slope is − 3 and the y -intercept is 1 , so the answer is − 3 .
Explanation
Identifying the Equation The equation of the line is given as y = − 3 x + 1 . We need to identify the slope and y -intercept of this line.
Understanding Slope-Intercept Form The equation is in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y -intercept.
Determining the Slope and y-intercept Comparing the given equation y = − 3 x + 1 with the slope-intercept form y = m x + b , we can identify the slope and y -intercept. The coefficient of x is the slope, so m = − 3 . The constant term is the y -intercept, so b = 1 .
Stating the Results Therefore, the slope of the line is − 3 and the y -intercept is 1 .
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 in modeling various phenomena and making predictions.
The slope of the line given by the equation y = − 3 x + 1 is − 3 , and the y -intercept is 1 . Therefore, option A is correct. To graph the line, start at the point (0, 1) and use the slope of − 3 to find additional points.
;
