Question

For triangle GHI with vertices G(4,1), H(5,-4), and I(2,-8), what is the equation of the line representing side GH?

A) y = x
B) y = -x
C) y = 3x
D) y = -3x

Answer 1

The equation of the line representing side GH is y = -5x + 21.

Step-by-step explanation:

The equation of the line representing side GH can be found using the slope-intercept form of a linear equation, which is y = mx + b.

The slope, m, can be found by calculating the difference in y-coordinates divided by the difference in x-coordinates between points G and H.

The y-coordinate difference is -4 - 1 = -5 and the x-coordinate difference is 5 - 4 = 1. Therefore, the slope is -5/1 = -5.

Using the slope-intercept form, we substitute the slope (-5) and one of the points (G: (4,1)) into the equation.

This gives us y = -5x + b. To find b, we substitute the x and y values of point G and solve for b.

Plugging in x = 4 and y = 1, we get 1 = -5(4) + b. Solving for b, we get b = 21.

Finally, substituting the values of m and b into the equation, we have the equation of the line representing side GH as y = -5x + 21.