Question

3. ** Write and graph the equation of the line that is perpendicular to the line shown on the coordinate grid below, and goes through the point (4,4) V (4,4) 1 (3,-1)4 I

Answer 1

y = -1/5 x + 4 4/5

Step-by-step explanation:

The given points: (3, -1) and (4, 4)

We apply the slope formula to get the slope. Then we insert into the equation of line.

slope = change in y/change in x

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ x_1=3,y_1=-1,x_2=4,y_2\text{ = }4 \end{gathered}`

slope = (4 -(-1))/(4-3) = (4+1)/(4-3)

slope = 5/1 = 5

The equation of line: y = mx + c

using any of the given points and m, we would get the intercept (c).

Using point (x, y): (3, -1)

-1 = 5(3) + c

-1 = 15 + c

c = -1-15

c = -16

The equation the line: y = 5x + (-15)

y = 5x - 15

For a line to be perpendicular to another, the slope of one must be equal to the negative reciprocal of the other.

First slope = 5

reciprocal of the slope = 1/5

negative reciprocal of the slope = -1/5

The point for the other line is (4, 4)

`\begin{gathered} Point\text{ slope formula: }y-y_1=m\mleft(x-x_1\mright) \\ y-4\text{ = -1/5(x - 4)} \end{gathered}`

y -4 = -1/5 x + 4/5

y = -1/5 x + 4/5 + 4

y = -1/5 x + 4 4/5

Hence, the equation of the line that is perpendicular to the line shown on the coordinate grid is y = -1/5 x + 4 4/5