goteachmaths.co.uk Identifying y=mx+c

08 December 2018 y=mx+c

𝒚 = m𝒙 + c y-intercept? Gradient? Do you know the name for this line? By the end of the lesson we will be able to mathematically name a line.

Where a line cuts the y-axis. y-intercept: Where a line cuts the y-axis. y-intercept is: +2

Where a line cuts the y-axis y-intercept: Where a line cuts the y-axis y-intercept is: -3

A y-intercept is: +4 B y-intercept is: +2 C y-intercept is: 0 D y-intercept is: -4 E y-intercept is: -3 F y-intercept is: -8

Gradient: A number that describes how steep a line is. The mountain has a bigger gradient than the hill. (It’s steeper.)

Rise Gradient = Run 6 Gradient = 3 Gradient = 2 Run 6 5 4 Rise 3 2 1 1 1 2 3 4 5 6 7

The gradient is the same anywhere on a line.

Gradient = 2 1 across, 2 up

Gradient = 3 1 across, 3 up

Like reading, we measure gradient left to right! 1 across, 2 down

The Equation (name) of a Straight Line m is the gradient. 𝒚 = 2𝒙 𝒚 = 3𝒙 + 5 𝒚 = 4𝒙 - 2 𝒚 = m𝒙 + c 𝒚 = 𝟏 𝟐 𝒙 𝒚 = 𝟒 𝟑 𝒙 c is the y-intercept 𝒚 = 6𝒙 - 10 𝒚 = 𝒙 + 1

𝒚 = m𝒙 + c The gradient = 2 𝒚 = 2𝒙 + 5 The y-intercept = +5

11/11 = 1 2/2 = 1 1 y = 1x + 1 y = x+ 1

Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation =

y = 2x y = 2x + 2 y = 2x + 2 y = 0.5x + 3 y = 2x + 2 y = 4x - 1 Gradient = Y-Intercept = Equation = y = 2x Gradient = Y-Intercept = Equation = y = 2x + 2 y = 2x + 2 Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = y = 0.5x + 3 y = 2x + 2 y = 4x - 1 y = 2x + 2 Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = y = -4x + 4 Gradient = Y-Intercept = Equation = Gradient = Y-Intercept = Equation = y = -2x + 1 y = 0.25x - 5 y = 1/3x + 2

y = 3x + 3 y = 3x + 3 y = 3x + 3 y = 3x + 3 y = 3x + 3 y = 3x + 3 A A Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 3x + 3 y = 3x + 3 y = 3x + 3 A A A Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 3x + 3 y = 3x + 3 y = 3x + 3

y = 2x y = 2x y = 2x y = 2x y = 2x y = 2x B B B B B B Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 2x y = 2x y = 2x B B B Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 2x y = 2x y = 2x

y = x + 3 y = x + 3 y = x + 3 y = x + 3 y = x + 3 y = x + 3 C C C C C Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = x + 3 y = x + 3 y = x + 3 C C C Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = x + 3 y = x + 3 y = x + 3

y = 3x - 2 y = 3x - 2 y = 3x - 2 y = 3x - 2 y = 3x - 2 y = 3x - 2 D D Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 3x - 2 y = 3x - 2 y = 3x - 2 D D D Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 3x - 2 y = 3x - 2 y = 3x - 2

y = 2x + 3 y = 2x + 3 y = 2x + 3 y = 2x + 3 y = 2x + 3 y = 2x + 3 E E Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 2x + 3 y = 2x + 3 y = 2x + 3 E E E Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = 2x + 3 y = 2x + 3 y = 2x + 3

y = -3x + 3 y = -3x + 3 y = -3x + 3 y = -3x + 3 y = -3x + 3 F F F Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = -3x + 3 y = -3x + 3 y = -3x + 3 F F F Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = -3x + 3 y = -3x + 3 y = -3x + 3

y = -2x - 2 y = -2x - 2 y = -2x - 2 y = -2x - 2 y = -2x - 2 G G G Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = -2x - 2 y = -2x - 2 y = -2x - 2 G G G Y-intercept = Gradient = Y-intercept = Gradient = Y-intercept = Gradient = y = -2x - 2 y = -2x - 2 y = -2x - 2

I can draw a linear graph, but I can’t identify the gradient or Comment in your book. I can draw a linear graph, but I can’t identify the gradient or y-intercept. I can draw a linear graph and I can identify the y-intercept. I can draw a linear graph and I can identify the equation of a line.

Extension! y = mx + c What can you tell about the coefficient (m) of the equation? How does it change the line? What can you tell about c? What does it tell you about where the line is? 𝒚 = 1/4𝒙 𝒚 = -2/5𝒙 - 3 𝒚 = -0.3𝒙 + 4

Is this coordinate on the graph? 𝒚 = 𝒙 (2, 0) 𝒚 = 2𝒙+1 (3, 7) 𝒚 = 3𝒙-2 (5, 10) 𝒚 = 1/2𝒙 - 3 (5, -0.5) 𝒚 = -4𝒙+3 (-2, 11) 2𝒚 = 4𝒙-8 (3, 2)