What is the equation of the line passing through (2, 0) and perpendicular to          2x + 5y − 8 = 0?1 pointA. 2x + 5y + 5 = 0B. 5x − 2y − 10 = 0C. 2x − 5y − 2 = 0D. 5x + 2y − 4 = 0

First, we need to find the slope of the given line. The equation of the line is in the form Ax + By = C. We can rewrite it in the slope-intercept form (y = mx + b) to find the slope.

The given line is 2x + 5y - 8 = 0.

Rearranging it to y = mx + b form gives us y = -2/5x + 8/5.

So, the slope of the given line is -2/5.

The slope of the line perpendicular to this line is the negative reciprocal of -2/5, which is 5/2.

Now, we use the point-slope form of the line equation to find the equation of the line passing through (2, 0) and having slope 5/2.

The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes.

Substituting the given values, we get y - 0 = 5/2(x - 2).

Simplifying this gives us 2y = 5x - 10.

Rearranging terms, we get 5x - 2y - 10 = 0.

So, the equation of the line passing through (2, 0) and perpendicular to 2x + 5y - 8 = 0 is 5x - 2y - 10 = 0.

Therefore, the correct answer is B. 5x - 2y - 10 = 0.

First, we need to find the slope of the given line. The equation of the line is in the form Ax + By = C. We can rewrite it in the slope-intercept form (y = mx + b) to find the slope.

The given equation is 2x + 5y - 8 = 0.

Rearranging it to the slope-intercept form gives us:

5y = -2x + 8

y = -2/5x + 8/5

So, the slope of the given line is -2/5.

The line perpendicular to this line would have a slope that is the negative reciprocal of -2/5, which is 5/2.

The equation of the line with slope m passing through the point (x1, y1) is given by y - y1 = m(x - x1).

Substituting m = 5/2, x1 = 2, and y1 = 0 into this equation gives us:

y - 0 = 5/2(x - 2)

Simplifying this gives us:

2y = 5x - 10

Rearranging terms gives us the equation of the line in the standard form:

5x - 2y - 10 = 0

So, the equation of the line passing through (2, 0) and perpendicular to 2x + 5y - 8 = 0 is 5x - 2y - 10 = 0.

Therefore, the correct answer is B. 5x - 2y - 10 = 0.