Answer:
2
Step-by-step explanation:
To find the slope of Line 1 passing through points (-4, 8) and (12, -2) , we use the formula for slope m :
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let's calculate the slope of Line 1:
[tex]m_1 = \frac{-2 - 8}{12 - (-4)} \\\\ m_1 = \frac{-2 - 8}{12 + 4} \\\\ m_1 = \frac{-10}{16} \\\\ m_1 = -\frac{10}{16} \\\\ m_1 = -\frac{5}{8} \\\\[/tex]
The slope of Line 1, m_1 , is [tex]-\frac{5}{8} .[/tex]
Since Line 2 is perpendicular to Line 1, the slopes of Line 1 and Line 2 are negative reciprocals of each other.
The negative reciprocal of [tex]-\frac{5}{8} is \frac{8}{5} .[/tex]
Answer:
The slope of line 2 is 8/5.
Step-by-step explanation:
First, a line perpendicular to another line has a negative inverse slope to the slope of the other line.
The inverse is the same as dividing 1 by the given value. It can also be found by flipping the values of the numerator and denominator. The inverse of 3 is 1/3. We must also multiply our number by -1 to fufill the "negative" part of "negative inverse".
This means that if the first line has a slope of 2/3, then the perpendicular line must have a slope of -3/2.
To find the perpendicular line's slope, first find the slope of line 1.
We are given two points on line 1, which we can use in the slope formula:
(y₂ - y₁) / (x₂ - x₁)
Substitute our coordinates into our equation.
(-2-8) / (12- -4)
Subtracting by a negative number is the same as adding the two values together. This means that 12- -4 = 12 + 4 = 16.
-10/16 is our slope, but it is not in simplest form. We can do so by dividing both sides by 2/2, which does not affect the final value because any number over itself is equal to 1. Dividing by 1 will always yield the same value, by the Identity Property of Multiplication.
[tex]\frac{-10}{16}\div\frac{2}{2} =\frac{-5}{8}[/tex]
So the slope of line 1 = -5/8.
We established earlier that the slope of a perpendicular line is the negative inverse of the line it is perpendicular to, so we can now use that logic to find the slope of line 2.
The negative version of -5/8 is 5/8 because a negative multiplied by another negative yields a positive number. The inverse of 5/8 is 8/5.
The slope of line 2 is 8/5.