The only way you can say that is from the general rule that perpendicular lines have
negative reciprocal slopes. You certainly can't demonstrate it from the slopes of the
axes themselves, because the slope of the x-axis is zero, and the slope of the y-axis
is either infinite or else undefined, whichever term bothers you less.
0
We know that the slope of a line is (Changes in y)/(Changes in x). Does the y-axes has changes in y? No. This means that y-axis does not have a slope. The same thing is for x-axis.
Undefined slopes belong to lines that are vertical. These lines do not cross the y-axis, but do cross the x-axis. Therefore, the equation for these lines are always: x = # (where # is the value at which the line is crossing the x-axis).
Yes the product will be negative, in fact the product will equal negative one (-1). Think about this. Suppose you have a line y = mx + b, and you want to rotate it 90° counterclockwise. This new line would be like in a coordinate system (x',y') [the x' and y' are called x-prime and y-prime, and differentiate between the original and new coordinate system], where the x' axis runs along the y axis in the positive y direction, and the y' axis runs along the x axis in the negative x direction. So the new line y' = mx' + b with x' = y and y' = -x, is: -x = my + b. Solving for y in the new equation gives y = (-1/m)x - (b/m). So the new slope (-1/m) times the original slope (m) equals (-m/m) = -1, as long as the original slope was not zero.
The x-axis comes first. because x comes before y.
It is not, because the slope of the y-axis is not defined.
The slope of the x-axis is 0 and the y-axis does not have a slope. For all pairs of perpendicular lines, other than those parallel to the axes, the product of their slopes is -1.
The slope of the x-axis is zero.The slope of the y-axis is "undefined" or "infinity". Whichever term you use, it's nota number that can participate in ordinary arithmetic operations. So the product ofthe slopes can't be calculated.For any other two perpendicular lines, the product of their slopes is -1 .
0
We know that the slope of a line is (Changes in y)/(Changes in x). Does the y-axes has changes in y? No. This means that y-axis does not have a slope. The same thing is for x-axis.
1
Slopes of line perpendicular to the x-axis are undefined.
Undefined slopes belong to lines that are vertical. These lines do not cross the y-axis, but do cross the x-axis. Therefore, the equation for these lines are always: x = # (where # is the value at which the line is crossing the x-axis).
No, the axis must be specified: torque = (distance from the axis) X (force). (X is the vector cross-product in this case - meaning the angle also matters.)No, the axis must be specified: torque = (distance from the axis) X (force). (X is the vector cross-product in this case - meaning the angle also matters.)No, the axis must be specified: torque = (distance from the axis) X (force). (X is the vector cross-product in this case - meaning the angle also matters.)No, the axis must be specified: torque = (distance from the axis) X (force). (X is the vector cross-product in this case - meaning the angle also matters.)
If they are perpendicular, the product of their slopes should be -1 -1*X = -1 X = 1 The other line has slope 1
Yes the product will be negative, in fact the product will equal negative one (-1). Think about this. Suppose you have a line y = mx + b, and you want to rotate it 90° counterclockwise. This new line would be like in a coordinate system (x',y') [the x' and y' are called x-prime and y-prime, and differentiate between the original and new coordinate system], where the x' axis runs along the y axis in the positive y direction, and the y' axis runs along the x axis in the negative x direction. So the new line y' = mx' + b with x' = y and y' = -x, is: -x = my + b. Solving for y in the new equation gives y = (-1/m)x - (b/m). So the new slope (-1/m) times the original slope (m) equals (-m/m) = -1, as long as the original slope was not zero.
Solve both equations for y in terms of x: y = (-2)x+5 y = (-1/2)x+1/2 Multiply the slopes together: (-2) X (-1/2) = 1 In order for the lines to be perpendicular, the product of the slopes would have had to equal -1, but it equals 1, so they're not perpendicular.