Question

We identify the y-intercepts $-3$and slopes $4$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.

Short answer

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

(b) the equation of the given term is $y=4x-3$.

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

Step-by-step solution

Part (a) Step 1: Given Information

We are given that the y-intercept is $-3$ and slope is $4$ and we have to find out about the slope nature.

Part (a) Step 2: Explanation

Now, as we know that the given slope is$4$i.e., it is positive which means that y-value increases by $4$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 $-3$and slope is $4$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$4$and y-intercept is $-3$.

put these value in equation 1...

we get,$y=4x-3$

Hence, this is the required equation.

Part (c) Step 1: Given Information

We are given that the y-intercept is $-3$ and slope is $4$ 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$y=4x-3$

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

Case I-

Put x=$0$and find the value of y,

we get localid="1650836146737" $y=4\left(0\right)-3=3$so, the point is localid="1650836151611" $(0,3)$.

Case II-

Put y=localid="1650836157042" $11$and find the value of x.

we get localid="1650836161559" $11=4x-3$

rearranging localid="1650836165761" $x=2$so, the point islocalid="1650836170025" $(2,11)$

Now plot these two points on the graph

Hence this is the required graph.