Linear Relations Grade 10 connections

y = mx ±b We know that the equation of any straight line, called a linear equation, can be written as: y = mx ±b. We have been calling m “rate of change”. In grade 10, they will refer to m as the slope of the line and b as the y-intercept. The y-intercept of the line is the value of y at the point where the line crosses the y axis. Obviously, the value of x at that point will be 0 x

Finding slope One of the most important properties of a straight line is in how it angles away from the horizontal. This concept is reflected in something called the "slope" of the line. Let's take a look at the straight line equation  y =  2/3x – 4.   Often, in grade 10, you will only work with two points to find the slope and create a line on a graph. Pick two x's and solve for each corresponding y: If, say, x = 3, then y = ( 2/3 )(3) – 4 = 2 – 4 = –2. If, say, x = 9, then y = ( 2/3 )(9) – 4 = 6 – 4 = 2.  So the ordered pairs (3, –2) and (9, 2) are points on the line and you will be able to draw the line for the equation y = 2/3x – 4.

This year, we learned two ways to find the rate of change: using a table of values to find the change in y and x values, and using the fraction ∆𝑦 ∆𝑥 to calculate m In grade 10, to find the slope, you will use the following formula: The subscripts 1 and 2 merely indicate that you have a "first" point (whose coordinates are subscripted with a "1") and a "second" point (whose coordinates are subscripted with a "2"). The subscripts indicate nothing more than the fact that you have two points to work with. It is entirely up to you which point you label as "first" and which you label as "second". For computing slopes with the slope formula, the important thing is that you subtract the x ‘s and y 's in the same order.

In grade 10, they will also call the slope “rise over run” . So, using the grade 10 slope formula: you will be able to easily find the slope. After all, it’s the same technique we used this year: calculating the change in y values divided by the change in your x values. In grade 10, they will also call the slope “rise over run” . No need to panic. When you think of it: the change in y values represents the “rise” up the y axis, the change in x values represents the “run” across the x axis.

What will the graph look like for y =  2/3x  – 4 You can use the two points we calculated earlier: (3, –2) and (9, 2) You can create a table of values: You can use the original linear equation to figure out the rise and run y =  2/3x  – 4 Y intercept slope

Find only the slope of the line passing through the points (–1, 1) and (–2, –3).

What information do you know about this line? Point A: Point B: Slope: y intercept: Equation: A B

What is the slope of this line? Point A: Point B: Slope: Equation: y intercept:

With resources from: www.thedeepdarkdepthsofmrs.swayzie’sbrain.yikes LOL www.math.com www.purplemath.com www.sparknotes.com http://brozanskaalgebra1.wikispaces.com