Q. 4.17 - Elementary Statistics

Question

We identify the y-intercepts $-2$ and slopes $-3$ 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 $y=-3x-2$.

(c) See the graph in Step $6$.

Part (a) Step 1: Given Information

We are given that the y-intercept is $-2$ and slope is $-3$ and we have to find out about the slope nature.

Part (a) Step 2: Explanation

Now, as we know that the given slope is $-3$ i.e., it is positive which means that y-value decreases by $3$ 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 $-2$ and slope is $-3$ 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 $-3$ and y-intercept is $-2$.

put these value in equation 1...

we get, $y=-3x-2$

Hence, this is the required equation.

Part (c) Step 1: Given Information

We are given that the y-intercept is $-2$ and slope is $-3$ 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 $y=-3x-2$

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

Case I-

Put x=$0$ and find the value of y,

we get $y=-3\left(0\right)-2=-2$ so, the point is $(0,-2)$.

Case II-

Put y=$1$ and find the value of x.

we get $1=-3x-2$

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

Now plot these two points on the graph.

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Hence this is the required graph.