What is the equation of the line that is perpendicular to the line defined by the equation 2y = 3x + 1 and goes through the point (3, 2)? options:
y = - 1/3 x + 3
y = -2/3x + 4
y = 1/3x – 1
y = 2x – 4
y = 6x + 5

Step-by-step explanation:

In order to determine the perpendicular slope to the given line, we first need to determine the slope of the given line, which is not apparent in its current form. We need to solve the equation for y to determine the slope:

2y = 3x + 1 in slope-intercept form is

.  Therefore, the perpendicular slope, the opposite reciprocal of the given slope of 3/2 is -2/3. Passing through the point (3, 2):

and

 so

, the second choice down.

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