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:

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form