BNU1501
Basic Numeracy
ASSIGNMENT 04
Semester 1 – 2023
Due Date: 28 April 2023
Question 1
What is the gradient and the y-intercept for a straight line with the equation 𝑦𝑦 = 6𝑥𝑥 − 5?
[1] Slope = 6, y-intercept = 5
[2] Slope = 6, y-intercept = -5
[3] Slope = 5, y-intercept = -6
[4] Slope = 5, y-intercept = 6
The given equation is in the form y = mx + b, where m is the slope and b is the y-intercept.
Comparing with the given equation 𝑦 = 6𝑥 − 5, we can see that the slope is 6 and the y-
intercept is -5.
Therefore, the correct answer is [2] Slope = 6, y-intercept = -5.
1
,Question 2
A straight line crosses the x-axis at (3, 0) and the y-axis at (0, 2). What is the y-intercept for this
line?
[1] y-intercept = 3
[2] y-intercept = 0
[3] y-intercept = 6
[4] y-intercept: 2
The line crosses the y-axis at (0, 2), which means that the y-intercept is 2.
Therefore, the correct answer is [4] y-intercept: 2.
Question 3
Calculate the gradient of a straight line which passes through points (4, 9) and (8, 12).
[1]
[2] −
[3]
[4] −
The formula for calculating the gradient of a straight line passing through two points
(x1, y1) and (x2, y2) is: gradient = (y2 - y1) / (x2 - x1)
Using the given points (4, 9) and (8, 12), we can plug in the values to get:
gradient = (12 - 9) / (8 - 4) =
Therefore, the gradient of the straight line is 3/4, which corresponds to answer [1]
2
, Question 4
The nearest point to the line 3𝑥𝑥 + 4𝑦𝑦 = 25 from the origin is
[1] (-4, 5)
[2] (3, 4)
[3] (3, -4)
[4] (3, 5)
To find the nearest point to the line from the origin, we need to find the point on the line
that is closest to the origin. This point will lie on the perpendicular line drawn from the
origin to the given line.
The given equation is 3𝑥𝑥 + 4𝑦𝑦 = 25, which can be rewritten in slope-intercept form as:
𝑦𝑦 = (-3/4)𝑥𝑥 + (25/4)
The slope of this line is -3/4, which means that the slope of the perpendicular line is 4/3.
Let (x,y) be the coordinates of the point on the given line that is closest to the origin. Since
this point lies on the perpendicular line, its coordinates must satisfy the equation:
𝑦𝑦 = (4/3)𝑥𝑥
We also know that this point lies on the given line 3𝑥𝑥 + 4𝑦𝑦 = 25, so we can substitute 𝑦𝑦
= (4/3)𝑥𝑥 into this equation to get: 3𝑥𝑥 + 4(4/3)𝑥𝑥 = 25
Simplifying this equation, we get: 25𝑥𝑥 = 100
𝑥𝑥 = 4
Plugging this value back into 𝑦𝑦 = (4/3)𝑥𝑥, we get:
𝑦𝑦 = (4/3)(4) = 16/3
Therefore, the nearest point to the line from the origin is (4, 16/3), which is closest to
answer [3] (3, -4). However, none of the answer choices match exactly with the calculated
point, so the closest answer choice is [3] (3, -4).
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Basic Numeracy
ASSIGNMENT 04
Semester 1 – 2023
Due Date: 28 April 2023
Question 1
What is the gradient and the y-intercept for a straight line with the equation 𝑦𝑦 = 6𝑥𝑥 − 5?
[1] Slope = 6, y-intercept = 5
[2] Slope = 6, y-intercept = -5
[3] Slope = 5, y-intercept = -6
[4] Slope = 5, y-intercept = 6
The given equation is in the form y = mx + b, where m is the slope and b is the y-intercept.
Comparing with the given equation 𝑦 = 6𝑥 − 5, we can see that the slope is 6 and the y-
intercept is -5.
Therefore, the correct answer is [2] Slope = 6, y-intercept = -5.
1
,Question 2
A straight line crosses the x-axis at (3, 0) and the y-axis at (0, 2). What is the y-intercept for this
line?
[1] y-intercept = 3
[2] y-intercept = 0
[3] y-intercept = 6
[4] y-intercept: 2
The line crosses the y-axis at (0, 2), which means that the y-intercept is 2.
Therefore, the correct answer is [4] y-intercept: 2.
Question 3
Calculate the gradient of a straight line which passes through points (4, 9) and (8, 12).
[1]
[2] −
[3]
[4] −
The formula for calculating the gradient of a straight line passing through two points
(x1, y1) and (x2, y2) is: gradient = (y2 - y1) / (x2 - x1)
Using the given points (4, 9) and (8, 12), we can plug in the values to get:
gradient = (12 - 9) / (8 - 4) =
Therefore, the gradient of the straight line is 3/4, which corresponds to answer [1]
2
, Question 4
The nearest point to the line 3𝑥𝑥 + 4𝑦𝑦 = 25 from the origin is
[1] (-4, 5)
[2] (3, 4)
[3] (3, -4)
[4] (3, 5)
To find the nearest point to the line from the origin, we need to find the point on the line
that is closest to the origin. This point will lie on the perpendicular line drawn from the
origin to the given line.
The given equation is 3𝑥𝑥 + 4𝑦𝑦 = 25, which can be rewritten in slope-intercept form as:
𝑦𝑦 = (-3/4)𝑥𝑥 + (25/4)
The slope of this line is -3/4, which means that the slope of the perpendicular line is 4/3.
Let (x,y) be the coordinates of the point on the given line that is closest to the origin. Since
this point lies on the perpendicular line, its coordinates must satisfy the equation:
𝑦𝑦 = (4/3)𝑥𝑥
We also know that this point lies on the given line 3𝑥𝑥 + 4𝑦𝑦 = 25, so we can substitute 𝑦𝑦
= (4/3)𝑥𝑥 into this equation to get: 3𝑥𝑥 + 4(4/3)𝑥𝑥 = 25
Simplifying this equation, we get: 25𝑥𝑥 = 100
𝑥𝑥 = 4
Plugging this value back into 𝑦𝑦 = (4/3)𝑥𝑥, we get:
𝑦𝑦 = (4/3)(4) = 16/3
Therefore, the nearest point to the line from the origin is (4, 16/3), which is closest to
answer [3] (3, -4). However, none of the answer choices match exactly with the calculated
point, so the closest answer choice is [3] (3, -4).
3
