Q. 4.19 - Elementary Statistics

Question

We identify the y-intercepts $0$and slopes $-0.5$ respectively, without graphing the equation-

(a) determine whether it slopes is upward, slopes downward, or is horizontal, without graphing the equation.

(b) find its equation.

(c) use two points to graph the equation.

Step-by-Step Solution

Answer

a) The slope of given intercept and slope is downward.

(b) the equation of the given term is $y=-0.5x$.

(c) See the graph in Step $6$

Part (a) Step 1: Given Information

We are given that the y-intercept is $0$ and slope is $-0.5$ and we have to find out about the slope nature.

Part (a) Step 2: Explanation

Now, as we know that the given slope is $-0.5$ i.e., it is positive which means that y-value decreases by $0.5$ for every increase in x by $1$ unit and whenever the slope will be negative it will be downward as it always decrease the value of y.

Hence, the slope is downward.

Part (b) Step 1: Given Information

We are given that the y-intercept is $0$ and slope is $-0.5$and we have to find out about the slope nature.

Part (b) Step 2: Explanation

Now, as we know that the general equation of line is 

 $y=mx+c$let this be equation $1$....

where m is the slope and c is the y-intercept.

and as we are given that slope is $-0.5$ and y-intercept is $0$.

put these value in equation $1$..

we get, $y=-0.5x$

Hence, this is the required equation.

Part (c) Step 1: Given Information

We are given that the y-intercept is $0$ and slope is $-0.5$and we have to find out about the slope nature.

Part (c) Step 2: Explanation

Now, we have find out the equation in part (b)

which is $y=-0.5x$

To find out the points it should satisfy the equation..

Case I-

Put x=$0$ and find the value of y,

we get $y=-0.5\left(0\right)$ so, the point is $(0,0)$.

Case II-

Put y=$1$ and find the value of x.

we get $1=-0.5x$

rearranging $x=-2$ so, the point is $(-2,1)$.

Now plot these two points on the graph

Hence this is the required graph