Ahomeowner is cleaning the sidewalk in front of his house. the sidewalk is 45 ft long. he cleans it at a rate of 6 ft/h.

which sketch represents that situation?

4th sketch represents the situation correctly.

Step-by-step explanation:

Given:

Length of sidewalk = 45 ft

Rate of cleaning = 6 ft/hr

From the given data we can conclude the following.

1) As rate is given in 'ft/hr' we can say that the y-axis represents the length of sidewalk being cleaned and x-axis represents the time elapsed.

2) The y-intercept of the line must be as the cleaner starts cleaning the 45 ft long sidewalk and this decreases as he continues cleaning.

3) The rate of cleaning tells us about the slope of the line. The slope of the line must be =-6 as the length of the uncleaned sidewalk decreases at the rate of 6 ft/hr.

The 4th sketch represents the situation correctly as:

a) it has a y-intercept of

b) it has a slope=-6  [Using the two points on the sketch we find the slope using slope formula.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)