Q2.Plot three points with second coordinate equal yo (1.3) and join them .
Q3.What is the slope of the line y= -1/3x +3
(B)Does it slope upwards?
(C) It is steeper than the line y=-1/2x -5?
Give reason for your answer.
Q4.The equation of the straigth line P is 3y-2x=7
I) Find the y - itercept of p.
II)Find the x- intercept of p.
III)Find whether the points A (2,-3/2) B (-3/2,-5/2) are on p. IV) Make a rough sketch of p.
V) write the equation of p in standard form.
VI) What is the gradient of p?
VII) If (k,4) and (t + 1,t - 1) are points on p find k and t.
Q5.The equation of line l is 5x - 3y = 7 .What is the gradient of L?
Q2. points with equal y-coordinate are all in the same horizontal line: y = 1.3
Q3.
slope = -1/3, so it slopes down.
the other line has slope -1/2
So, is -1/3 greater or less than -1/2?
Q4.
y-intercept is at x=0
x-intercept is at y=0
check the points to see whether they fit the equation. If so, they are on the line.
standard form is Ax+By=C
the gradient is -A/B
3y-2x=7
3*4-2k = 7, so k=19/2
3(t-1)-2(t+1) = 7, so t=12
Q5. -5/-3
Q2: To plot three points with the second coordinate equal to 1.3 and join them, you can follow these steps:
1. Choose any three distinct x-coordinates for the points. Let's say you choose x1, x2, and x3.
2. Since the second coordinate should be 1.3 for all three points, the coordinates would be (x1, 1.3), (x2, 1.3), and (x3, 1.3).
3. Plot these three points on a coordinate plane.
4. Connect these three points with a straight line segment.
Q3: The equation of the line y = -1/3x + 3 represents a linear equation in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
To find the slope of the line, you can compare the equation with the standard slope-intercept form (y = mx + b) and identify the coefficient of x. In this case, the coefficient of x is -1/3, which represents the slope of the line.
The slope of the line y = -1/3x + 3 is -1/3.
(B) Since the slope is negative (-1/3), the line slopes downwards, not upwards.
(C) To compare the steepness of the line y = -1/3x + 3 and the line y = -1/2x - 5, you can compare the slopes. The slope of the line y = -1/2x - 5 is -1/2.
Since -1/2 > -1/3, the line y = -1/2x - 5 is steeper than the line y = -1/3x + 3.
Q4: Let's break down the questions one by one to find the answers.
I) To find the y-intercept of the line, you substitute x = 0 in the equation 3y - 2x = 7 and solve for y.
3y - 2(0) = 7
3y = 7
y = 7/3
The y-intercept of the line P is (0, 7/3).
II) To find the x-intercept of the line, you substitute y = 0 in the equation 3y - 2x = 7 and solve for x.
3(0) - 2x = 7
-2x = 7
x = -7/2
The x-intercept of the line P is (-7/2, 0).
III) To check if points A(2, -3/2) and B(-3/2, -5/2) are on the line P, you substitute their x and y values in the equation 3y - 2x = 7.
For point A:
3(-3/2) - 2(2) = 7
-9/2 - 4 = 7
-9/2 - 8/2 = 7
-17/2 ≠ 7
Therefore, point A is not on the line P.
For point B:
3(-5/2) - 2(-3/2) = 7
-15/2 + 3/2 = 7
-12/2 = 7
-6 ≠ 7
Therefore, point B is not on the line P.
IV) To make a rough sketch of the line P, you can plot its y-intercept (0, 7/3) and x-intercept (-7/2, 0) on a coordinate plane and draw a straight line passing through these two points.
V) To write the equation of line P in standard form, you need to rearrange the equation 3y - 2x = 7 so that the coefficients of x and y are integers and the constant term is positive.
3y - 2x = 7
3y = 2x + 7
2x - 3y = -7
The equation of line P in standard form is 2x - 3y = -7.
VI) The gradient (or slope) of line P can be found by rearranging the equation in the slope-intercept form (y = mx + b), where m is the slope.
3y - 2x = 7
3y = 2x + 7
y = (2/3)x + 7/3
The gradient (m) of line P is 2/3.
VII) Given that (k, 4) and (t + 1, t - 1) are points on line P, we can substitute their x and y values in the equation 3y - 2x = 7 and solve for k and t.
For (k, 4):
3(4) - 2k = 7
12 - 2k = 7
-2k = -5
k = 5/2
For (t + 1, t - 1):
3(t - 1) - 2(t + 1) = 7
3t - 3 - 2t - 2 = 7
t - 5 = 7
t = 12
Therefore, k = 5/2 and t = 12.
Q5: The equation of line l is given as 5x - 3y = 7. To find the gradient of line l, rearrange the equation in slope-intercept form (y = mx + b), where m is the slope.
-3y = -5x + 7
y = (5/3)x - 7/3
The gradient (or slope) of line l is 5/3.