The equation $(y+2)=-1 / 3(x-4)$ is in point-slope form. Fill in the blanks below to describe how to graph the equation.
Plot the point $\qquad$ , then move $\qquad$ unit(s) down and $\qquad$ unit(s) to the right to find the next point on the line.
A. $(4,-2)$, three, one
B. $(-2,4)$, one, three
C. $(2,4)$, one, three
D. $(4,-2)$, one, three
Answer (2)
Identify the point ( 4 , − 2 ) from the given equation.
Identify the slope − 3 1 from the given equation.
Plot the point ( 4 , − 2 ) .
Move 1 unit down and 3 units to the right to find the next point on the line.
The answer is: Plot the point ( 4 , − 2 ) , then move 1 unit(s) down and 3 unit(s) to the right to find the next point on the line.
Explanation
Analyze the equation The given equation is in point-slope form: ( y + 2 ) = − 3 1 ( x − 4 ) . We need to identify the point and the slope to describe how to graph the equation.
Recall point-slope form The point-slope form of a linear equation is given by y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is a point on the line and m is the slope of the line. Comparing this with the given equation ( y + 2 ) = − 3 1 ( x − 4 ) , we can identify the point and the slope.
Identify the point and slope From the given equation, we have y − ( − 2 ) = − 3 1 ( x − 4 ) . Thus, the point on the line is ( 4 , − 2 ) and the slope is − 3 1 .
Describe how to graph the equation To graph the equation, we first plot the point ( 4 , − 2 ) . The slope is − 3 1 , which means that for every 3 units we move to the right, we move 1 unit down. So, we move 1 unit down and 3 units to the right to find the next point on the line.
State the final answer Therefore, the correct answer is: Plot the point ( 4 , − 2 ) , then move 1 unit(s) down and 3 unit(s) to the right to find the next point on the line.
Examples
Understanding point-slope form is useful in many real-world scenarios. For example, imagine you are tracking the descent of a hot air balloon. If you know the balloon's altitude at one point in time and its rate of descent (slope), you can use the point-slope form to predict its altitude at any other time. This is a practical application of linear equations in physics and engineering, where understanding rates of change is crucial for making predictions and informed decisions. The point-slope form helps to model and analyze these situations effectively.
To graph the equation ( y + 2 ) = − 3 1 ( x − 4 ) , plot the point ( 4 , − 2 ) and then move 1 unit down and 3 units to the right to locate the next point on the line. The correct option is A. ( 4 , − 2 ) , three, one.
;
