Question

Which equation represents a line that is perpendicular to line FG​

Answer 1

Explanation:

Answer 2

Note: You missed to add some basic information of the perpendicular line or missed the answer options, hence I am solving using a sample equation but it would clear your concept.

Answer:

Please check the attached graph.

Explanation:

We know the slope-intercept form of line equation is

`y = mx+b`

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

Given the points

• F(1, 8)

• G(-3, -4)

Finding the slope between F(1, 8) and G(-3, -4)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-4\right)`

`m=(-4-8)/(-3-1)`

`m=3`

Thus, the slope of the line FG = m = 3

From the given line, we can also determine the y-intercept 'b' by setting x = 0 and checking the corresponding y value.

i.e. at x = 0, y = 5

Thus, y-intercept b = 5

so substituting m = 3 and b = 5 in the slope-intercept form

y = mx+b

y = 3x+5

Therefore, the equation of line FG will be:

• y = 3x+5

Please check the attached diagram, where the red line represents the line y=3x+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.

Slope of Perpendicular line = -1/m = -1/3

Thus, any line with the slope m = -1/3 would be the line that will be perpendicular to line FG​

Let say the line with the slope m = -1/3 and y-intercept 2

y = -1/3x + 5

Please check the attached graph, the blue line is representing the perpendicular line y = -1/3x + 5 to line FG

The graph of both lines is clearly representing that the line y = -1/3x + 5 is perpendicular to line FG.