Straight line Summary

Equations of Straight Lines4.1 THIS IS NOT HOMEWORK

1. Find the equation of the line parallel to the given line which passes through the given point. Give your answer in the form $ay+bx=c$

1. $3x-4y=3$ through (2,-1)
2. $5y-4x=12$ through (-3,-2)
3. $3x+4y=4$ through (1,1)
4. $5x+2y=8$ through (1,0)

[8 marks]

2. Find the equation of the line perpendicular to the given line which passes through the given point. Give your answer in the form $ay+bx+c=0$

1. $3x+2y=6$ through (5,1)
2. $5y-4x=2$ through (-3,3)
3. $y+3x=6$ through (5,0)
4. $4x+2y=5$ through (14,2)

[8 marks]

3.

1. Find the gradient of the line
2. Using the previous part and the coordinates of one of the points on the line, work out the equation of the line

[6 marks]

4. Find the equation of the line which passes through (-4,5) and (4,-7). Give your answer in the form $ax+by+c=0$

[3 marks]

5. Find the gradient and y intercept of the line $4x-3y=6$

[2 marks]

6. Find the equation of the line which is perpendicular to the line $2y-3x=10$ and passes through the point (2,-5). Give your answer in the form $ay+bx+c=0$

[4 marks]

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Books on proof

• Proof
• "Are you sure? Learning about proof

4.1 Homework 3

Homework 3: To be done neatly in the front of your books.
TOTAL 24 marks

1. Jon is twice the age of his son. 9 years ago he was three times the age of his son. How old is Jon's son currently?

[3 marks]

2. Show all your working out and leave answers as mixed numbers where needed:

1. $2\dfrac{4}{5} \times 3\dfrac{1}{3}$
2. $2\dfrac{1}{6} \div 4\dfrac{1}{3}$

[4 marks]

3.

The graph shows a plot of $y=x^3+x^2-6x-1$.

1. Find the values of x for which the gradient is 0
2. Use the plot to estimate the gradient when $x=0$

[4 marks]

4. Expand $(x+h)^4$ and use the result to find the gradient function for $y=x^4$

[5 marks]

5. Find the equation of a line which is parallel to the line $4x-3y=6$ but goes through the point (-2,7). Give your answer in the form $ay+bx=c$

[4 marks]

6. Find the equation of the line which is perpendicular to the line $3y-2x=12$ and passes through the point (-2,5). Give your answer in the form $ay+bx+c=0$

[4 marks]

4.1 Gradients Worksheet

A* Gradients of Lines and Curves 40 Marks

1. Find the equation of the line parallel to the given line which passes through the given point. Give your answer in the form $ay+bx=c$

1. $3x-4y=12$ through (4,-1)
2. $5y-2x=10$ through (-4,2)
3. $3x+5y=12$ through (5,0)
4. $4x+2y=5$ through (1,1)

[8 marks]

2. Find the equation of the line perpendicular to the given line which passes through the given point. Give your answer in the form $ay+bx+c=0$

1. $2x+3y=6$ through (6,1)
2. $3y-4x=5$ through (-4,-3)
3. $5y+3x=8$ through (2,0)
4. $4x-2y=3$ through (1,0)

[8 marks]

3.

The graph shows a plot of a cubic function.

1. Find the values of x for which the gradient is 0
2. Draw a tangent line at x=1 and use this to estimate the gradient

[4 marks]

4.

The graph shows a plot of a quadratic function.

1. Find the value of x for which the gradient is 0
2. Draw a tangent line at x=2 and use this to estimate the gradient

[4 marks]

5. Start by expanding $(x+h)^2$ and subsequently multiplying by $(x+h)$ to find an expression for $(x+h)^5$. Use the result to find the gradient function for $y=x^5$

[5 marks]

6. Find the gradient funtion for $y=x^2+x$ by looking at the limit of the following as $h\rightarrow 0$ \[ \dfrac{(x+h)^2+(x+h)-(x^2+x)}{h}\]

[5 marks]

7. Can you conjecture a result about the gradient function for $y=x^n$? Can you prove this result?

[6 marks]