VCE 11 MM Unit 1 SOLUTIONS
SHEET 1.1Linear FunctionsANSWERS
1 / Solve the linear equation:/
2 / Solve the linear equation:
/ )
3 / Solve the linear equation:
/
4 / Use the formula, , to find an exact value for when L = 160 and g = 10. /
5 / Use the formula, , to find a value for when , and g = 10. /
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6 / Find the gradient of the straight line passing through the points (–3, 8) and (5, –2). / Gradient = = = =
7 / Find the gradient of the straight line having an x-intercept of –2 and a y-intercept of 4. / The two points are (–2, 0) and (0, 4).
Gradient = = = = 2
8 / What is the gradient and y-intercept of the graph with equation y = 2x – 8? / Gradient = 2 and y-intercept = –8
9 / What is the gradient and y-intercept of the graph with equation 5x – 3y – 6 = 0? / Rearrange equation to make y the subject.
5x – 6 = 3y
Gradient is and y-intercept is –2.
10 / Which of these graphs are parallel (have the same gradient)?
a)3x – 4y – 4 = 0
b)4y – 3x – 6 = 0
c)6x – 8y – 6 = 0
d)2y – 6x – 12 = 0 / Rearrange each equation to make y the subject.
a)3x – 4y – 4 = 0
3x – 4 = 4y
Gradient =
b)4y – 3x – 6 = 0
4y = 3x + 6
Gradient =
c)6x – 8y – 6 = 0
6x – 6 = 8y
Gradient =
d)2y – 6x – 12 = 0
2y = 6x + 12
y = 3x + 6 = 0Gradient = 3
Graphs (a), (b) and (c) are parallel as they all have the same gradient.