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Given 2 points, how do you calculate the equation of a straight line?

Remember that the equation of a straight line function is: ax+c. a= change of y/ change of x The steps to follow are:1- find the gradient of the slope2- replace the equation by values coming from any of the ...
ZJ
Answered by Zachary J. • Maths tutor
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Simplify the algebraic expression: (3x^2-7x-6)/(x^2-6x+9)

We start by noticing that both the numerator and denominator are expressions which can be factorised into brackets. Starting with the numerator, we multiply the coefficient of x^2 and the constant term toget...
EG
Answered by Emily G. • Maths tutor
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Solve the simultaneous equations: 3x − y = 23 2x + 3y = 8

Write the 2 equations above each other: 3x-y=23 2x+3y=8First we want to remove the y terms to be able to find out x, so multiply the top equation by 3 9x-3y=69 2x+3y=8Now that we have -3y on the top and -3y ...
JB
Answered by Jessica B. • Maths tutor
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n is an integer greater than 1. Prove algebraically that n^2 – 2 – (n – 2)^2 is always an even number.

1) Expand the brackets: (n-2) 2 = (n-2)(n-2) = n 2 - 2n - 2n +4 = n 2 - 4n + 4 2) Substitute this into the original expression: n 2 - 2 - (n 2 - 4n +4) = n 2 - 2 - n 2 + 4n - 4 = 4n - 6 3) Reduce this: 4n - ...
JM
Answered by James M. • Maths tutor
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Solve the simultaneous equations, x^2+y^2=41, and y=2x-3

STEP 1) First, substitute 2x-3 into the quadratic equation, replacing y, which works out as x 2 +(2x-3) 2 =41 STEP 2) Now, expand the bracket, (2x-3) 2 , firstly by writing it in an easier way, (2x-3)(2x-3),...
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Answered by Hannah N. • Maths tutor
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