Given: y=1/2x-6y=12x−6
Compare to the standardised form of y=mx+cy=mx+c
color(blue)("Teaching bit about gradient")Teaching bit about gradient
Where m->" gradient"->("change in y")/("change in x")m→ gradient→change in ychange in x
Note that the gradient is consequential to reading left to write on the x-axis. This is important as it indicates if the graph is like 'going up a hill' or if it is like 'going down a hill' left to right.
Negative gradient is going down y->" becomes less"y→ becomes less
Positive gradient is going up y->" becomes greater"y→ becomes greater
So we have m=("change in y")/("change in x")->1/2m=change in ychange in x→12
As this is positive the graph 'goes up' reading left to right.
m=("change in y")/("change in x")->1/2 m=change in ychange in x→12 means that for every change of 1 in the y-axis the x-axis changes by 2.
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color(blue)("Answering the question")Answering the question
color(brown)("Determine the y-intercept")Determine the y-intercept
The plot crosses the y-axis at x=0x=0 so by substitution we have:
y_("intercept")=1/2(0)-6yintercept=12(0)−6
y_("intercept")=0-6yintercept=0−6
y_("intercept")=-6yintercept=−6
y_("intercept")->(x,y)=(0,-6) color(green)(" Notice "-6" is the constant"yintercept→(x,y)=(0,−6) Notice −6 is the constant
" "color(green)(darr) ↓
" "y=mxcolor(green)(+c) y=mx+c
color(brown)("Determine the x-intercept")Determine the x-intercept
The plot crosses the x-axis at y=0y=0 so by substitution we have:
0=1/2x_("intercept")-60=12xintercept−6
Add 6 to both sides
6=1/2x_("intercept")6=12xintercept
Multiply both sides by 2
12=x_("intercept")12=xintercept
x_("intercept")->(x,y)=(12,0)xintercept→(x,y)=(12,0)
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