Extensive explanation given - using first principles method
Note that the shortcut method is based on the outcome of first principle method
Target: Manipulate the given equation into the form of y=mx+c
where m is the gradient and c is the y-intercept.
The 32y is positive so we need to keep the y on that side of the equation.
To get rid of the x on the left we change it to 0
What we do to one side of the equation we also do to the other.
Add x to both sides.
32y−x+x = 2+x
But −x+x=0
32y+0=2+x
Note that x+2 has the same value as 2+x
32y=x+2
To 'get rid' of the 32 change it to 1 as 1×y=y
Multiply both sides by 23
32×23×y=23(x+2)
y=23x+43→ 23 is the gradient (slope)
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The y-axis crosses the x-axis at x=0 so substitute 0 for x
yintercept=23(0)+43 = 43
The x-axis cross the y-axis at y=0 so substitute 0 for y
0=23x+43
Subtract from both sides 43
−43=23x
Multiply both sides by 32
x=32×(−43)
x=−(33×42)
xintercept=−2
