The equation of a line is .
For the line find:
A new line, intersects the -axis at (4, 0) and is perpendicular to .
Find:
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The equation of a line is .
For the line find:
A new line, intersects the -axis at (4, 0) and is perpendicular to .
Find:
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The coordinates of point are and the coordinates of point B are . is the midpoint of .
Find the coordinates of .
The line passes through and .
Find the gradient of .
Find the equation of the line Give your answer in the form , where and are integers.
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The coordinates of point are and the coordinates of point are . is the midpoint of .
Find the coordinates of .
The line passes through the points and .
Find the equation of . Give your answer in the form of .
A new line, , is the perpendicular bisector to .
Find the equation of . Give your answer in the form of .
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Plumber A charges a fixed fee of $25 plus $15 per hour.
Using for the number of hours a job takes, and for the total cost of a job, in dollars, from Plumber A, write down an equation connecting and .
A job takes the plumber seven hours.
Calculate the total cost of the job.
Plumber B charges a fixed fee of $20 plus $16 per hour.
Using for the number of hours a job takes, and for the total cost of a job, in dollars, from Plumber B, write down an equation connecting and .
Determine which plumber would be the cheapest for a job taking six hours.
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The diagram below shows the line , which intersects the -axis at A and the -axis at B.
Find the equation of Give your answer in the form of .
Find the length of [AB].
A second line, is parallel to and intersects the -axis at C.
Find the equation of Give your answer in the form , where and are integers.
Find the coordinates where l2 intersects the y-axis.
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Photocopy shop A charges $122 for 115 copies, and $190 for 200 copies.
Assuming a linear relationship, find
Photocopy shop B charges $0.82 per copy and a fixed fee of $25.50.
State which photocopy shop is cheaper to make 220 copies.
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A family can be supplied with electricity by two companies that have different pricing structures:
Company A: Fixed fee of $25/month and $0.2 per kWh consumed.
Company B: Fixed fee of $10/month and $0.22 per kWh consumed.
Determine the equation of the cost function for both companies, where the total monthly cost is a function of the monthly electricity consumption in kWh.
Calculate the monthly energy consumption that results in the same monthly cost from both companies.
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Ardie’s monthly expenditure, is a linear function of his monthly income, . Ardie’s monthly expenditure is $1000 when his monthly income is $1200 and his monthly expenditure increases by $60 for every $150 increase in his monthly income.
Write an expression connecting Ardie’s monthly expenditure, with his monthly income, .
Calculate Ardie’s monthly expenditure when his monthly income is $1885. Give your answer to the nearest dollar.
Find Ardie’s monthly income when his monthly expenditure is $1070. Give your answer to the nearest dollar.
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The diagram below represents a mountain with a west facing slope and an east facing slope labelled and respectively.
Horizontal scale: 1 unit represents 100 m.
Vertical scale: 1 unit represents 100 m.
Find the gradient of the west facing slope.
The gradient of the east facing slope in the diagram is .
Find the total distance to hike over the mountain in km.
Suggest a reason as to why the actual total distance hiked may be greater than the distance found in part (b).
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The straight lines and are shown in the diagram below intercepts the -axis at and the -axis at and intercepts the -axis at and the -axis at .
Giving your answer in the form , find:
Find the area of the shaded region.
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A line passing through the origin , is perpendicular to a line with equation
The two lines meet at point . is a point such that OP : PR = 3 : 1.
Find the equation of the perpendicular line and hence, the co-ordinates of point R.
Find the coordinates of P.
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