Question

Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid. A coordinate plane with a line passing through two points at 0,3 and 5,2. What is the equation of line t in standard form?

Option 1: 5x - y = 15
Option 2: -5x - y = 15
Option 3: x - 5y = -75
Option 4: x + 5y = 75

Answer 1

The equation of the perpendicular line t that passes through the point (4, 5) is 5x - y = 15, which is derived by finding the negative reciprocal of the original line's slope and using the point-slope form.

Step-by-step explanation:

The question asks for the equation of line t which is perpendicular to a given line on a coordinate grid and passes through the point (4, 5). The given line passes through points (0, 3) and (5, 2), from which we can find the slope (m) to be (2 - 3) / (5 - 0) = -1/5. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of line t will be the negative reciprocal of -1/5, which is 5. Using the point-slope form, the equation of line t passing through (4, 5) can be written as (y - 5) = 5(x - 4), which simplifies to y = 5x - 20 + 5, or y = 5x - 15 when rearranged into slope-intercept form. Converting this into standard form, we get -5x + y = -15 or equivalently 5x - y = 15, which matches Option 1. Therefore, the equation of line t in standard form is 5x - y = 15.