4. Using the graph on the right, a) Graph x

4. Using the graph on the right, a) Graph $x - 2y = 8$ using x- and y-intercepts. [3 marks] b) Graph the lines $x = 5$ and $y = -3$. Label. [2 marks] 3. Identify the following pairs of lines as parallel or perpendicular or neither. [2 marks] a) $y = 2x + 3$ $y = frac{1}{2}x - 5$ b) $2x - 5y = 7$ $4x - 10y = 9$ 4. Does the data in each table represent a linear or non-linear relationship? Explain. [3 marks] egin{array}{|c|c|} hline x & y \ hline -2 & 1 \ hline 0 & -5 \ hline 1 & -8 \ hline end{array} 5. Determine the equation for the following linear relations described below. Express your answers in slope-intercept form, $y = mx + b$. a) parallel to $y = -3x + 5$ and passes through the point $(-2, 9)$. [3 marks]

Transcript

00:01 So the first question we're given has to do with graphing a linear equation.

00:06 And it gives us the equation x minus 2y equals 8.

00:10 And they want us to graph it using the x and y intercepts.

00:12 So the x and y intercepts are where the opposite value is equal to 0.

00:16 So for example, if i plugged in 0 for y, that would negate this piece here in the middle.

00:21 And i would have just x equals 8.

00:22 So my x intercept is 8.

00:24 If i repeated the process and plugged in 0 for x, i would have negative 2y equals 8.

00:29 And so i could divide by negative 2 to isolate y, and i get y equals negative 4.

00:34 So my x intercept is 8 .0, and my y intercept would be 0 negative 4.

00:40 So in graphing this, i could just plot those two points and connect them to draw that line.

00:46 So 8 .0 would be over here, and then negative 4, i'm sorry, 0 negative 4 would be about here.

00:54 And if i sketch the line, it's going to look something like that.

00:57 Continuing with the same graphing idea, we have two other equations that they want us to graph x equals 5 and y equals negative 3.

01:05 So if i go to an x value of 5, 1, 2, 3, 4, 5, it's right there.

01:11 I want to draw the line such that every point on that line has an x value of 5.

01:15 So, for example, this is 5 .0, i would have 5 1, 5, 5, 2, 5, 5, 4, and so on.

01:21 And the same in the negative direction, 5 negative 1, 5 negative 2, 5 negative 3.

01:25 So the line x equals 5 is a vertical line where every x value is equal to 5.

01:33 The second one, y equals negative 3.

01:36 If i go to negative 3 on my y axis, again, i want every point on the line that i draw to have a y value of negative 3.

01:42 So that y intercept is 0 negative 3.

01:45 So 1, negative 3, 2, negative 3, 3.

01:48 Same in the opposite direction.

01:50 Negative 1, negative 3, negative 3, negative 2, negative 3, negative 3.

01:53 So the line y equals negative 3 is a horizontal line where every y value on that line is negative 3.

02:03 Moving on to the next set of questions, they give us two equations and they want us to identify if the pair of equations is parallel perpendicular or neither.

02:12 So if we look at a, they give us the equation y equals 2x plus 3.

02:18 And the second one they give us is y equals 1 half x.

02:23 I think it's minus five.

02:25 So to determine if it's parallel or perpendicular, we just need to look at the slope.

02:29 So we're looking at the coefficient to x.

02:32 If it's the same number, they're parallel.

02:34 Because if two lines are at the same slant or the same slope, they're never going to touch.

02:39 They would be parallel.

02:41 For two lines to be perpendicular, they need to be negative reciprocals of each other, meaning that they need to be going in opposite directions and they need to be negative, like they need to be able to cross.

02:51 So they would be going at the same slant, but going in the opposite direction...

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