james is taking a test in his geomtery class. His teacher asked him to determine the equation of the line perpendicular to the line 2x-y=-3 and passing through the point (8,2) , which line should he choose.

A. y+ 1/2x=6
B.y+2x=18
C. y-2x=-14
D. y +1/2x=9

perpendicular means slopes are negative-reciprocals

easiest to see in point-slope ... y = 2x + 3

so -1/2 is the new slope ... A or D

plug in the point (8,2) to check which one

thank you !!!

To determine the equation of the line perpendicular to 2x - y = -3 and passing through the point (8, 2), we first need to find the slope of the given line.

The given line is in the form of Ax + By = C, where A, B, and C are constants. To make it easier to find the slope, let's rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with 2x - y = -3:
Add y to both sides: 2x = y - 3
Rearrange: y = 2x - 3

Now we can see that the slope of the given line is 2. Since we want a line that is perpendicular, we need to find the negative reciprocal of this slope.

The negative reciprocal of 2 is -1/2.

So, the slope of the line perpendicular to the given line is -1/2.

Now, let's check each answer choice to see which one has a line with a slope of -1/2 and passes through the point (8, 2).

A. y + 1/2x = 6:
This equation is in standard form, so let's convert it to slope-intercept form.
Subtract 1/2x from both sides: y = -1/2x + 6
The slope of this line is -1/2, but does it pass through (8, 2)?

Plug in x = 8 and y = 2 into the equation:
2 = -1/2 * 8 + 6
2 = -4 + 6
2 = 2

Since both sides are equal, (8, 2) is a point on this line.

B. y + 2x = 18:
This equation is not in slope-intercept form. Let's convert it.
Subtract 2x from both sides: y = -2x + 18
The slope of this line is -2, not -1/2.

C. y - 2x = -14:
This equation is not in slope-intercept form. Let's convert it.
Add 2x to both sides: y = 2x - 14
The slope of this line is 2, not -1/2.

D. y + 1/2x = 9:
This equation is in standard form, so let's convert it to slope-intercept form.
Subtract 1/2x from both sides: y = -1/2x + 9
The slope of this line is -1/2, but does it pass through (8, 2)?

Plug in x = 8 and y = 2 into the equation:
2 = -1/2 * 8 + 9
2 = -4 + 9
2 = 5

Since both sides are not equal, (8, 2) is not a point on this line.

Therefore, the correct answer is option A: y + 1/2x = 6.