Q. 4.15 - Elementary Statistics

Question

We identify the y-intercepts $5$ and slopes $2$ 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 upward.

(b) the equation of the given term is $y=2x+5$.

(c) See the graph in Step $6$.

Part (a) Step 1: Given Information

We are given that the y-intercept is $5$ and slope is $2$ and we have to find out about the slope nature.

Part (a) Step 2: Explanation

Now, as we know that the given slope is $2$ i.e., it is positive which means that y-value increases by $2$ for every increase in x by $1$ unit and whenever the slope will be positive it will be upward as it always increase the value of y.

Hence, the slope is upward.

Part (b) Step 1: Given Information

We are given that the y-intercept is $5$ and slope is $2$ and we have to find out about the equation.

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 $2$and y-intercept is $5$.

put these value in equation 1...

we get, $y=2x+5$.

Hence, this is the required equation.

Part (c) Step 1: Given information

We are given that the y-intercept is $5$ and slope is $2$ and we have to plot the graph using two points.

Part (c) Step 2: Explanation

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

which is $y=2x+5$

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

Case I-

Put x=$0$ and find the value of y,

we get $y=2\left(0\right)+5=5$ so, the point is $(0,5)$.

Case II-

Put y=$7$ and find the value of x.

we get $7=2x+5$

rearranging $x=1$ so, the point is $(1,7)$

Now plot these two points on the graph

Hence this is the required graph.