b)The water line is given by the equation
y=-2/3x-12
Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point (-4,-10)?
c)What is the slope and y-intercept of the line in part b? How do you know?
d)Suppose you want to add a sprinkler system, and the location of one section of the sprinkler line can be described by the equation
Y= -1/2x-4
Complete the table for this equation.
x y (x,y)
-1
-2
-4
2
8
e)What objects might be in the way as you lay the pipe for the sprinkler?
b) Plug in x=-4 and y=-10 into the equation
= -(2/3)x -12
If the equation is not satisfied, then there is no water line below.
(c) The slope is ths coefficient of the "x" term. The y-intercept is the constant term (-12 in this case). It is the value of y when x = 0.
(d) You should be able to do this yourself. All you do is pick a series of x values and calculate the corresponding y values. One point is x=0, y=-4
b) To determine if you can place the pink flamingo lawn ornament at the point (-4, -10), we need to check if it lies on the water line given by the equation y = -2/3x - 12.
To verify if the point (-4, -10) lies on the water line, substitute the x and y values into the equation:
-10 = -2/3(-4) - 12
Solve this equation to find out if the point (-4, -10) satisfies the equation.
c) The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
In the equation y = -2/3x - 12, the coefficient of x (-2/3) represents the slope, and the constant term (-12) represents the y-intercept.
To determine the slope and y-intercept, compare the equation to the slope-intercept form and identify the corresponding values.
d) For the equation y = -1/2x - 4, we need to complete the table by substituting different x-values and calculating the corresponding y-values.
To fill in the table, substitute the given x-values into the equation and calculate the corresponding y-values:
x y (x,y)
-1
-2
-4
2
8
Substitute each x-value into the equation and calculate the corresponding y-value to complete the table.
e) To determine which objects might be in the way as you lay the pipe for the sprinkler described by the equation y = -1/2x - 4, you need to consider the objects that intersect or lie close to the line of the equation.
Since the equation represents the location of one section of the sprinkler line, objects that are near or intersect the line might include trees, shrubs, rocks, fences, or any other physical obstructions that lie in the vicinity of the line described by the equation.