91Ó°ÊÓ

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

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.

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

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.

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

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 localid="1650858085825" $(0,-2)$.

Case II-

Put y=localid="1650857715419" $1$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.