Show that the slope of the line through the points (6,7) and (12,15) is perpendicular to the slope of the line given by the equation 4y+3x-5=0. Be sure to justify you answer.
Please walk me through to the answer, first get 10 points!
Please walk me through to the answer, first get 10 points!
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First find the slope of the line with the points (6,7) and (12,15).
The slope formula is y2-y1 / x2-x1.
So substitute the points to get 15-7 / 12 - 6.
Simplify to get. 8 / 6 then 4 / 3.
If a line is perpendicular to another the its slope is the opposite reciprocal of the other's slope. So if aforementioned line has a slope of 4/3 then the line its perpendicular to should have a slope of
- 3 / 4. (Opposite reciprocal of a number is what is multiplied to the number to get -1. To find this just switch the numerator and denominator and change the sign)
So let's see if the equation shows a line with a slope of -3 / 4.
In the slope intercept form y=mx+b, m is the slope.
So solve for y by subtracting 4y from both sides to get 3x - 5 = -4y.
Then divide both sides by -4 to get y = -3 / 4 x - 5/4
M is the slope and - 3 /4 x is m so -3/4x is the slope!
So both lines are perpendicular.
The slope formula is y2-y1 / x2-x1.
So substitute the points to get 15-7 / 12 - 6.
Simplify to get. 8 / 6 then 4 / 3.
If a line is perpendicular to another the its slope is the opposite reciprocal of the other's slope. So if aforementioned line has a slope of 4/3 then the line its perpendicular to should have a slope of
- 3 / 4. (Opposite reciprocal of a number is what is multiplied to the number to get -1. To find this just switch the numerator and denominator and change the sign)
So let's see if the equation shows a line with a slope of -3 / 4.
In the slope intercept form y=mx+b, m is the slope.
So solve for y by subtracting 4y from both sides to get 3x - 5 = -4y.
Then divide both sides by -4 to get y = -3 / 4 x - 5/4
M is the slope and - 3 /4 x is m so -3/4x is the slope!
So both lines are perpendicular.