Straight line graphs

Question 1

Which of the following points lie on the line $4x -5y = 1?$

Not correct. Choice (a) is false.

Try again, $(0, 1 ) 4$ is not on the line but $(-1 ,- 1)$ is on the line.

Not correct. Choice (b) is false.

Try again, $(4,3)$ is on the line but $1 (5 ,0)$ is not.

Not correct. Choice (c) is false.

Try again, $(-1 ,1)$ is not on the line but $1 (0,5)$ is on the line

Your answer is correct.

$(-1 ,- 1)$ is on the line since $4 × -1- 5 × -1 = -4 +5 = 1,$
and $(9,7)$ is on the line since $4 ×9 - 5× 7 = 36 - 35 = 1.$

Question 2

What is the gradient, $m ,$ of the line between the points $(-2 ,-1)$ and $(-5 ,6)?$

Not correct. Choice (a) is false.

Try again, recalling that $m = -y2--y1. x2 - x1$

Not correct. Choice (b) is false.

Try again and watch negative signs.

Your answer is correct.

$m = -6--(-1)- = -7-= - 7. - 5- (-2) -3 3$

Not correct. Choice (d) is false.

Try again, recalling that $y - y m = -2---1- x2- x1$ and watching negative signs.

Question 3

What is the equation of the line between the two points $(4,-2)$ and $(-2 ,3)?$

Not correct. Choice (a) is false.

Try again, watching signs carefully.

Your answer is correct.

$m = 3--(-2)-= -5 - 2- 4 6$ and so $y = -5 x+ b 6$ and we have that
$b = y+ 5x = -2 + 5 ×4 = --12+-20 = 8 6 6 6 6$ and so
$5 8 y = - -x+ - , 6 6$ hence $6y = -5x + 8$ and $5x+ 6y = 8.$

Not correct. Choice (c) is false.

Try again, $(- 2,3)$ is not on this line. You should try and calculate the equation of the line.

Not correct. Choice (d) is false.

Try again, and check the gradient.

Question 4

What is the gradient, $m ,$ and $y$ -intercept, $b,$ of the line $2x + 3y = 12?$

Your answer is correct.

We need to rearrange the equation to $3y = - 2x+ 12$ and then see that $y = - 2x + 4 3$ and $m = -2 3$ and $b = 4.$

Not correct. Choice (b) is false.

Try again, you need to rearrange the equation to the form $y = mx + b$ and then you can read the answer from the equation. You have just found the coefficient of $x$ for the gradient and the constant term for $b.$

Not correct. Choice (c) is false.

Try again, looking carefully at the signs

Not correct. Choice (d) is false.

Try again, you need to rearrange the equation to the form $y = mx + b$ and then you can read the answer from the equation. You seem to have made $x$ the subject of the equation.

Question 5

What is the equation of the line below?

Not correct. Choice (a) is false.

Try again, we know at least two points on the line $(- 1,0)$ and $(0,-2)$ so we can use these to find the equation of the line.

Not correct. Choice (b) is false.

Try again, look at the intercept

Not correct. Choice (c) is false.

Try again, look at the gradient.

Your answer is correct.

There are many ways of calculating the correct line but it passes through the points $(- 1,0)$ and $(0,-2)$
so $-2- 0 m = 0--(-1) =- 2$ and the $y$ -intercept is -2 so $y =- 2x- 2.$


		Faculty of Economics and Business MathQuiz