y = 0.5x + 1 x = -2, y = 0 x = -1, y = 0.5 x = 0, y = 1 x = 1, y = 1.5 x = 2, y = 2 Plot the points in the coordinate system, and draw the line, which is the line of the given equation.
if INVERSELY proportional then y = 1/X^2 ( that is, 1 divided by x squared) If X doubles then X SQUARED increases as 2 x 2 = 4 times SINCE Y = 1/x^2 then Y DECREASES 4 times
How about y = (x - 2)2 = x2 - 4x + 4 ? That is the equation of a parabola whose axis of symmetry is the vertical line, x = 2. Its vertex is located at the point (2, 0).
The equation "x plus 2y equals 5" is: x + 2y = 5 2y = 5 - x y = 5/2 - 1/2x y = -1/2x + 5/2
In general, if a line passes through the points (a, b) and (c, d), its equation can be written as:y - b = [(d - b)/(a - c)](x - a)In this case, however, the formula is not necessary -- and in fact, attempting to apply it in its current form would result in a division by zero error. Instead, however, we can simply note that from (-2, 9) to (-2, 7) the x-coordinate does not change. This can only be the case if the line is vertical, meaning that the x-coordinate never changes. The line can therefore be represented by the equation x = -2.
The whole line 'shifts up' by two units, and is parallel to the original line (same slope)
The diagonal line collapses into a single point on that line.
Imagine the set up: line 1 X line 2 X X line 3 X X X line 4 X X X X line 5 (empty) Move the pin from line 1 to the centre of line 5. line 1 (empty) line 2 X X line 3 X X X line 4 X X X X line 5 X Now move the 2 outer pins on line 4 to the outer position on line 2 line 1 (empty) line 2 X X X X line 3 X X X line 4 X X line 5 X And there you go. Except the spacings I used weren't saved. I hope you get the idea though!
If there are n scores and one score is changed by x then the mean changes by x/n.
5
x - y - 2 = 0-y = -x + 2y = x - 2The graph is a straight line. The slope of the line is [2].The line intersects the x-axis at [x=2], and the y-axis at [y=-2].
A vertical line that passes through -2 on the x-axis.
I understand this to mean x = 2. This is the vertical line passing through the (2, 0) or, alternatively, the vertical line passing through the point where x = 2 on the x-axis.
6
Because the inverse of a function is what happens when you replace x with y and y with x.
4
x-3y+2 = 4 -3y = -x+4-2 -3y = -x+2 y = 1/3x-2/3 Slope or gradient of the perpendicular line is -3 Use y-y1 = -3(x-x1) to find the perpendicular equation