Graph linear relations on the Cartesian plane; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution.
You should know.
You should know
Standard form
y=mx+c
$m$ is the GRADIENT. $c$ is the $y$ INTERCEPT.
Gradient from two points
m=x2−x1y2−y1
Rise over run.
Sign of the gradient
m>0risesm<0falls
Read the line left to right.
Parallel lines
m1=m2
Same gradient.
Perpendicular lines
m1×m2=−1
Gradients multiply to $-1$.
Worked example
e.g.y=3x−4
Read off the gradient. It is the number in front of xm=3
Read off the y intercept. It is the number on its ownc=−4
The gradient is positive, so the line risesm>0
The line crosses the y axis at −4(0;−4)
Practice
Write down the gradient and the y intercept:
1
y=2x+5
Answerm=2,c=5
2
y=−4x+1
Answerm=−4,c=1
3
y=21x−3
Answerm=21,c=−3
4
y=7−2x
Answerm=−2,c=7
5
2y=6x+4
Answerm=3,c=2
6
y=x
Answerm=1,c=0
7
3y=9x−12
Answerm=3,c=−4
8
y+2x=5
Answerm=−2,c=5
9
Is y=2x+1 parallel to y=2x−7?
AnswerYes, both have m=2
10
Is y=3x perpendicular to y=−31x?
AnswerYes, 3×−31=−1
Next step
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