1Sep 2303:21 p.m.Linear functionsDuring this lesson we will :• Explore the equation of a straight line.• Discover algebraic relations between pairs of parallel and perpendicular lines.• Explore the absolute value function and its properties.• Recognise and draw piecewise linear functions.
2Sep 2303:21 p.m.Distance between two pointsAB
4Sep 2303:21 p.m.Linear functionsThe graph is a straight line.
5Sep 2303:21 p.m.Gradient of a lineThe gradient of a line is a measure of its steepnessIfandpositive gradient negative gradient
6Sep 2303:21 p.m.horizontal lines have a gradient of 0 (zero)vertical lines have an undefined gradientparallel lines have equal gradientsthe gradients of perpendicular lines arenegative reciprocalsif the gradients are m1 and m2 then:or
7Sep 2303:21 p.m.Equations of linesThe equation of a line is an equation which states the connectionbetwen the x and y values for every point on the line.All vertical lines have equations of the form x = a , ( a is a constant)All horizontal lines have equations of the form y = c , ( c is a constant)slope-intercept form or explicit formgradienty-interceptgeneral form or implicit form(not a function)
8Sep 2303:21 p.m.Write down the gradient and y-intercept of these straightlines:y = 5x 22y = 1 6 x3x + 2y 8 = 0
9Sep 2303:21 p.m.Sketch the graphs of these equations:y = 2 x 1 3y + 2x 3 = 0 2y x + 1 = 0
10Sep 2303:21 p.m.Write down the equation of the straight line which passesthrough the points A (2,5) and B (6,17).
11Sep 2303:21 p.m.Find the explicit and implicit equations of the linethrough (-1,3) with a slope of 5.
12Sep 2303:21 p.m.Are L1 with equation 2x y + 2=0 and L2 with equationx + 4y 1 = 0 perpendicular lines?
13Sep 2303:21 p.m.Find the equation of the line through (1,-5) and (5,-2).Express the equation in the form Ax+By + C = 0, with A, B and Cinteger numbers.
14Sep 2303:21 p.m.InterceptsxinterceptyinterceptxyThe x-intercept is found by letting y =0.The y-intercept is found by letting x=0.
15Sep 2303:21 p.m.For the line with equation 2x - 3y =12, find axis intercepts.
16Sep 2303:21 p.m.Find the point of intersection of the lines :3x+4y=29 and 2x 5y=43x+4y=292x 5y=4
17Sep 2303:21 p.m.At the end of the lesson:Reproduce exactly this drawing on your GDC.
18Sep 2303:21 p.m.At the end of the lesson:Reproduce exactly this drawing on your GDC.
19Sep 2303:21 p.m.Can you give a formula for the followinggraph?
20Sep 2303:21 p.m. Piecewise linear functionsDraw the graph of: