The line y = x is a straight line of gradient '1' passing through the origin (0,0)
The line/curve y = x^(2) is 'bowl' shaped curve(parabola). with varying gradients, and just touching the origin (0,0).
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).
y = x/2 + 1 This is a line of the form y = mx + c When c = 1 it passes through the y-axis at y = 1 When m= 1/2 ( 0.5) it has a gradient of 1/2 )0.5) . For every two places along in 'x', you go up one place in 'y'. So to plot two point s When x = 1 ; y = 1/2 + 1 = 3/2 ( 1,3/2) When x - 2 ; y = 2/2 + 1 =. 1 + ` = 2 (2,2) et seq.,
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.
When the y-intercept of a line is changed, the entire line shifts vertically without altering its slope. If the y-intercept increases, the line moves upward; if it decreases, the line moves downward. The slope remains constant, meaning the angle of inclination relative to the x-axis does not change. This results in a parallel shift of the line along the y-axis.
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.
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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.
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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.
Because the inverse of a function is what happens when you replace x with y and y with x.
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