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There can be no line because there is no equation.

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Q: What is the line for x -2?

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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.

Any line of the form x = some_number. eg all the lines: x = -2 x = 0 x = 1.2 are perpendicular to y = -2.

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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!

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.

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

Any line of the form x = some_number. eg all the lines: x = -2 x = 0 x = 1.2 are perpendicular to y = -2.

Y = (X+4) / 2 is a straight line parallel to Y = 0.5 * X

On your graph, draw a vertical line through the point on the x-axis where [ x = -2 ]." X is less than or equal to -2 " is every point on that line and everything to the left of it.

I don't see an equals sign. Let's assume you mean y = x - 2. The gradient (coefficient) of x is +1. So for a line perpendicular this this, the gradient/slope need to be -1. So the equation of the line perpendicular to this is y = -x +c To find c, substitute x=-2 and y=4. This give c=2 So the line you want is y = -x +2

X intercept of -1 means that the line passes through (-1,0) y intercept of 2 means that the line passes though (0,2) The equation of this line is (y - y1) = [(y2 - y1)/(x2 - x1)] x (x - x1), that is y - 0 = [(2 - 0)/(0 + 1)] x (x +1), that is y = (2) x (x +1) or y = 2x + 2 Verification: In the equation y = 2x + 2 1) substitute -1 for x and y evaluates to 0; 2) substitute 0 for x in the equation and you get y as 2 which means this line passes through (-1,0) and (0,2)