Straight-line graphs – Year 10 GCSE maths worksheet with answers to download as PDF

Complete the table of values for \(y=2x-3\), plot the points and draw the line.

1. Complete the table.
2. Write down the gradient and the \(y\)-intercept.
3. Where does the line cross the \(x\)-axis?
4. Does the point \((5,8)\) lie on the line?

Work out the gradient of the line through each pair of points. Use \(m=\dfrac{y_2-y_1}{x_2-x_1}\).

1. \((1,3)\) and \((4,12)\)
2. \((-2,5)\) and \((2,-3)\)
3. \((0,4)\) and \((5,4)\)
4. What can you say about a vertical line through \((3,1)\) and \((3,7)\)?

Find the equation of each line in the form \(y=mx+c\).

1. gradient 3, passes through \((0,-2)\)
2. gradient \(-\tfrac12\), passes through \((4,1)\)
3. passes through \((1,5)\) and \((3,11)\)
4. passes through \((0,6)\) and \((3,0)\)

Parallel lines have the same gradient.

1. Which of these lines are parallel to \(y=3x-4\)? \(y=3x+5\), \(y=\tfrac13x\), \(y=2x-4\), \(2y=6x+1\)
2. Find the equation of the line parallel to \(y=3x-4\) passing through \((2,7)\).
3. Find the equation of the line parallel to \(y=-2x+1\) passing through \((1,1)\).
4. Write \(3x+y=9\) in the form \(y=mx+c\) and state its gradient.

Find the midpoint and length of each line segment AB.

1. A\((2,3)\) and B\((8,11)\)
2. A\((-1,2)\) and B\((4,14)\)
3. A\((0,0)\) and B\((5,12)\)
4. A\((-3,-1)\) and B\((5,5)\)

The line \(L\) has equation \(y=4x-5\).

1. Does \((3,7)\) lie on \(L\)?
2. Does \((2,4)\) lie on \(L\)?
3. Find \(y\) when \(x=-1\) and \(x\) when \(y=11\).
4. Find where \(L\) crosses both axes.

The cost \(C\) pounds of a taxi journey of \(d\) miles is \(C=2.5+1.2d\).

1. What does the \(y\)-intercept 2.5 represent?
2. What does the gradient 1.2 represent?
3. Find the cost of a 7.5 mile journey.
4. Find the distance travelled when the cost is £20.50.

Jade cycles to a friend’s house. Her journey is described below.

1. Find her speed for the first part in km/h.
2. What happens between 09:30 and 09:45?
3. Find her speed in the last part in km/h.
4. Find her average speed for the whole journey including the stop.

A water tank is filled steadily. After 2 minutes it holds 30 litres and after 6 minutes it holds 70 litres.

1. Find the rate of filling in litres per minute (the gradient).
2. Find the equation giving the volume \(V\) litres after \(t\) minutes.
3. How much water was in the tank at the start?
4. When will the tank hold 150 litres?

The graph of pounds (\(P\)) against euros (\(E\)) is a straight line through the origin. £50 is worth €58.

1. Find the gradient of the line \(E=mP\).
2. Write a formula for \(E\) in terms of \(P\).
3. Convert £325 into euros.
4. Convert €200 into pounds to the nearest penny.

A road sign warns of a hill with a gradient of 12%. This means a rise of 12 m for every 100 m travelled horizontally.

1. Write 12% as a fraction in its simplest form.
2. How high does the road rise over a horizontal distance of 450 m?
3. A road rises 36 m over 400 m horizontally. Find its percentage gradient.
4. Is the road in part (c) steeper than the 12% hill?

Degrees Fahrenheit and degrees Celsius are related by the straight line \(F=1.8C+32\).

1. What is the gradient and the \(F\)-intercept?
2. Find \(F\) when \(C=20\).
3. Find \(C\) when \(F=95\).
4. Where does the line \(F=1.8C+32\) cross the line \(F=C\)?

Hall A costs £40 plus £5 per hour. Hall B costs £15 per hour with no fixed charge. Let \(h\) be hours.

1. Write the cost lines \(y=\ldots\) for each hall.
2. Find where the lines cross.
3. Which hall is cheaper for a 3-hour party and for a 6-hour party?
4. Explain what the crossing point means.

Petrol costs £1.50 per litre. A graph of cost against litres is a straight line.

1. Does the line pass through the origin? Explain.
2. Write a formula for the cost \(C\) of \(L\) litres.
3. What is the gradient?
4. Mia pays £63 for petrol. How many litres did she buy?

Higher tier. Perpendicular lines have gradients whose product is \(-1\).

1. Find the gradient of a line perpendicular to \(y=2x+3\).
2. Find the equation of the line perpendicular to \(y=2x+3\) through \((4,1)\).
3. Find where the two lines meet.
4. Show that the lines \(y=3x-1\) and \(3y+x=6\) are perpendicular.

The table shows values for a straight line.

1. Show that the points lie on a straight line by finding the gradient between each pair.
2. Find the equation of the line.
3. Find \(y\) when \(x=10\).
4. Find \(x\) when \(y=-3\).

Triangle ABC has vertices A\((1,2)\), B\((7,2)\) and C\((4,8)\).

1. Find the midpoint of each side.
2. Find the length of AC to 1 decimal place and say what kind of triangle ABC is.
3. Find the area of the triangle.
4. Find the equation of the line AC.

The points P\((0,0)\), Q\((4,1)\), R\((6,5)\) and S\((2,4)\) are the corners of a quadrilateral.

1. Find the gradients of PQ and SR.
2. Find the gradients of QR and PS.
3. Explain why PQRS is a parallelogram.
4. Show that its diagonals PR and QS have the same midpoint.

The lines \(y=x\) and \(y=6-x\) and the \(y\)-axis enclose a triangle.

1. Find the point where the two lines cross.
2. Find where each line meets the \(y\)-axis.
3. Find the area of the triangle.
4. Find the perimeter to 1 decimal place.

Two lines are \(kx+2y=8\) and \(3x-y=1\).

1. Write each in the form \(y=mx+c\) and state the gradients.
2. Find \(k\) so that the lines are parallel.
3. Find \(k\) so that the lines are perpendicular.
4. For \(k=2\), find where the lines cross.