What is an equation of the line that passes through the point (2,-3) and is perpendicular to the line 2x+5y=10?

An equation of the line that passes through the point (2,-3) and is perpendicular to the line is:

Step-by-step explanation:

The slope-intercept form of the line equation

where m is the slope and b is the y-intercept

Given the line

Here, the slope = m = -2/5

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -2/5

perpendicular slope = – 1/m = -1/(-2/5) = 5/2

Using the point-slope form of the line equation

where m is the slope and (x₁, y₁) is the point

substituting the values m = 5/2 and the point (2,-3)

subtract 3 from both sides

Therefore, an equation of the line that passes through the point (2,-3) and is perpendicular to the line is:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .