Straight line graphs

Question 1

Which of the following points lie on the line $3x + 2y = 7?$

Not correct. Choice (a) is false.

Try again, $(2 ,1)$ is not on the line since $3 × 2+ 2× 1 = 6+ 2 = 8$ not 7 as required.
$(-1 ,5)$ is on the line since $3× - 1+ 2× 5 = -3+ 10 = 7.$

Not correct. Choice (b) is false.

Try again, $(1,2)$ is on the line since $3× 1 + 2× 2 = 3 + 4 = 7.$
$(0,7)$ is not on the line since $3 × 0+ 2× 7 = 0+ 14 = 14 ,$ not 7 as required.

Not correct. Choice (c) is false.

Try again, $(3,- 1)$ is on the line since $3× 3 +2 × -1 = 9- 2 = 7 .$
$(0, 7) 3$ is not on the line since $3× 0 + 2× 7 = 0+ 14= 4 2, 3 3 3$ not 7 as required.

Your answer is correct.

$(1,2)$ is on the line since $3× 1+ 2 × 2 = 3+ 4 = 7,$
and $(2,0.5)$ is on the line since $3× 2+ 2 ×0.5 = 6 + 1 = 7.$

Question 2

What is the gradient, $m$ of the line between the points $(-1,9)$ and $(2,5)?$

Not correct. Choice (a) is false.

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

Your answer is correct.

$-5--9--- --4-- 4 m = 2- (-1) = 2+ 1 = - 3 .$

Not correct. Choice (c) is false.

Try again, being careful with the signs.

Not correct. Choice (d) is false.

Try again, recalling that $m = y2--y1- x2 -x1$ and watching negative signs.

Question 3

What is the equation of the line between the two points $(2,1)$ and $(-1,8)?$

Not correct. Choice (a) is false.

Try again, $(- 1,8)$ is not on this line. You should try and calculate the equation of the line.

Not correct. Choice (b) is false.

Try again, $(- 1,8)$ is not on this line. You should try and calculate the equation of the line.

Your answer is correct.

$-8--1- 7 m = - 1- 2 = - 3$ and so $7 y = - 3x+ b$ and we have that
$b = y+ 7x = 8- 7 = 17 3 3 3$ and so $y = -7 x+ 17 , 3 3$

Not correct. Choice (d) is false.

Try again, and check your intercept.

Question 4

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

Not correct. Choice (a) 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. Check your signs.

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, you need to rearrange the equation to the form $y = mx + b$ and then you can read the answer from the equation.

Your answer is correct.

We need to rearrange the equation to gradient intercept form of the line, that is $y = mx + b$ .
So $2y = -3x + 12$ and then see that $3 y = -2 x+ 6$ so $3 m = -2$ and $b = 6.$

Question 5

What is the equation of the line below?

Your answer is correct.

There are many ways of calculating the correct line but it passes through the points $(-2 ,0)$ and $(0,4)$ so
$m = --4--0- = 2 0 -(-2)$ and the $y$ -intercept is 4 so $y = 2x+ 4,$ which can be rewritten as $y- 2x =4 .$

Not correct. Choice (b) is false.

Try again, look at the sign of the gradient.

Not correct. Choice (c) is false.

Try again, look at the gradient.

Not correct. Choice (d) is false.

Try again, we know at least two points on the line $(- 2,0)$ and $(0,4),$ so we can find the equation of the line.


		Faculty of Economics and Business MathQuiz