Find an equation in slope intercept form for the line through point p(-3, 2) and perpendicular to the line
containing the two points (2, 3) and (1, -2).

y=-1/5 x +7/5

Step-by-step explanation:

First lets find the slope for line containing the two points (2,3) and (1,2)

m=5

Two lines are perpendicular between each other if m1*m2=-1

we have one slope m1=5, we obtain m2= -1/5

Next we need to eval the equation for lines y=mx+b, where m= -1/5 using the point P(-3,2)

2=-1/5 * -3 +b

From that we obtain that b= 2-3/5=7/5

So the equation for the desired line is:

y=-1/5 x +7/5

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

49%

step-by-step explanation:

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