What is the equation of the line that passes through $(- 1, 1)$ $(-1,1)$ and is perpendicular to the line that passes through the following points: $(13, - 1), (8, 4)$ $(13,-1),(8,4)$ ?

Question

What is the equation of the line that passes through $(- 1, 1)$ $(-1,1)$ and is perpendicular to the line that passes through the following points: $(13, - 1), (8, 4)$ $(13,-1),(8,4)$ ?

2 Answers

Impact of this question

28490 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-25T11:43:11

See a solution process below:

Explanation:

First, we need to find the slope of the for the two points in the problem. The slope can be found by using the formula: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))$

Where $m$ $m$ is the slope and ( $x_{1}, y_{1}$ $color(blue)(x_1, y_1)$ ) and ( $x_{2}, y_{2}$ $color(red)(x_2, y_2)$ ) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{4 - - 1}{8 - 13} = \frac{4 + 1}{8 - 13} = \frac{5}{- 5} = - 1$ $m = (color(red)(4) - color(blue)(-1))/(color(red)(8) - color(blue)(13)) = (color(red)(4) + color(blue)(1))/(color(red)(8) - color(blue)(13)) = 5/-5 = -1$

Let's call the slope for the line perpendicular to this $m_{p}$ $m_p$

The rule of perpendicular slopes is: $m_{p} = - \frac{1}{m}$ $m_p = -1/m$

Substituting the slope we calculated gives:

$m_{p} = \frac{- 1}{- 1} = 1$ $m_p = (-1)/-1 = 1$

We can now use the point-slope formula to write an equation for the line. The point-slope form of a linear equation is: $(y - y_{1}) = m (x - x_{1})$ $(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))$

Where $(x_{1}, y_{1})$ $(color(blue)(x_1), color(blue)(y_1))$ is a point on the line and $m$ $color(red)(m)$ is the slope.

Substituting the slope we calculated and the values from the point in the problem gives:

$(y - 1) = 1 (x - - 1)$ $(y - color(blue)(1)) = color(red)(1)(x - color(blue)(-1))$

$(y - 1) = 1 (x + 1)$ $(y - color(blue)(1)) = color(red)(1)(x + color(blue)(1))$

We can also use the slope-intercept formula. The slope-intercept form of a linear equation is: $y = m x + b$ $y = color(red)(m)x + color(blue)(b)$

Where $m$ $color(red)(m)$ is the slope and $b$ $color(blue)(b)$ is the y-intercept value.

Substituting the slope we calculated gives:

$y = 1 x + b$ $y = color(red)(1)x + color(blue)(b)$

We can now substitute the values from the point in the problem for $x$ $x$ and $y$ $y$ and solve for $b$ $color(blue)(b)$

$1 = (1 \times - 1) + b$ $1 = (color(red)(1) xx -1) + color(blue)(b)$

$1 = - 1 + b$ $1 = -1 + color(blue)(b)$

$1 + 1 = 1 - 1 + b$ $color(red)(1) + 1 = color(red)(1) - 1 + color(blue)(b)$

$2 = 0 + b$ $2 = 0 + color(blue)(b)$

$2 = b$ $2 = color(blue)(b)$

Substituting this into the formula with the slope gives:

$y = 1 x + 2$ $y = color(red)(1)x + color(blue)(2)$

Answer 2 · 2017-08-25T11:50:16

The equation of the line is $x - y = - 2$ $x - y = -2$

Explanation:

The slope of the line passing through $(13, - 1) and (8, 4)$ $(13,-1) and (8,4)$ is

$m_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 + 1}{8 - 13} = \frac{5}{- 5} = - 1$ $m_1= (y_2-y_1)/(x_2-x_1)= (4+1)/(8-13)=5/-5 =-1$

The product of slopes of two perpendicular lines is $m \cdot m_{1} = - 1$ $m*m_1=-1$

$:. m= -1/m_1 =-1/-1=1$ . So the slope of the line passing

through $(-1,1)$ is $m=1$ .

The equation of the line passing through $(-1,1)$ is

$y-y_1=m(x-x_1) = y -1 = 1( x +1) = y-1 =x+1 or x-y = -2$ .

The equation of the line is $x - y = -2$ [Ans]

Science

Math

Humanities

... and beyond

What is the equation of the line that passes through $(- 1, 1)$ $(-1,1)$ and is perpendicular to the line that passes through the following points: $(13, - 1), (8, 4)$ $(13,-1),(8,4)$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the equation of the line that passes through (-1,1) (−1,1)(-1,1) and is perpendicular to the line that passes through the following points: (13,-1),(8,4) (13,−1),(8,4)(13,-1),(8,4) ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

What is the equation of the line that passes through $(- 1, 1)$ $(-1,1)$ and is perpendicular to the line that passes through the following points: $(13, - 1), (8, 4)$ $(13,-1),(8,4)$ ?