Question

Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line? line on coordinate plane passing through 0 comma 3 and 1 comma 1

Answer 1

To find the equation of Leo's line, which is perpendicular to the line passing through the points (0, 3) and (1, 1), we first need to determine the slope of the original line.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

For the points (0, 3) and (1, 1), the slope of the original line is:

m = (1 - 3) / (1 - 0)

= -2 / 1

= -2

Since the slope of the original line is -2, the perpendicular line will have a slope that is the negative reciprocal of -2.

The negative reciprocal of -2 is 1/2, which means the perpendicular line will have a slope of 1/2.

Now that we have the slope of the perpendicular line, we can use the point-slope form to find its equation. The point-slope form of a line is:

y - y₁ = m(x - x₁)

Substituting the point (F, G) and the slope 1/2, the equation becomes:

y - G = 1/2(x - F)

Therefore, the equation of Leo's line is:

y - G = 1/2(x - F)