Competency Test Chapter 3

Explanation
The gradient of a line is the measure of the steepness or slope of the line. To find the gradient of a line passing through two points, we use the formula: gradient = (change in y)/(change in x). In this case, the line passes through the points O and T(2, 5). To find the change in y, we subtract the y-coordinate of O from the y-coordinate of T, which gives us 5 - 0 = 5. To find the change in x, we subtract the x-coordinate of O from the x-coordinate of T, which gives us 2 - 0 = 2. Therefore, the gradient of the line is 5/2.

Explanation
To find the gradient (slope) of a line passing through two points, we can use the formula: gradient = (change in y)/(change in x). In this case, the change in y is 5 - 2 = 3, and the change in x is 2 - 4 = -2. Therefore, the gradient is 3/(-2) = -3/2.

Explanation
The statement (ii) is true because the line intersects the X-axis at a certain point. The statement (iii) is also true because the line intersects the Y-axis at the point (0, -3). Therefore, the correct answer is (ii) and (iii).

Explanation
The equation of a line parallel to another line can be found by using the same slope. The slope of the line passing through (2, 1) and (3, 6) can be calculated by using the formula (y2 - y1) / (x2 - x1). In this case, the slope is (6 - 1) / (3 - 2) = 5. Therefore, the equation of the line parallel to this line will also have a slope of 5. Option I is the correct answer because it provides an equation with a slope of 5.

Explanation
The equation for a line running through (5, -5) and (-5, 1) can be found using the slope-intercept form of a linear equation, which is y = mx + b. To find the slope (m), we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values, we get m = (1 - (-5)) / (-5 - 5) = 6 / (-10) = -3/5. Now we can substitute the slope and one of the given points into the equation to find the y-intercept (b). Using (5, -5), we have -5 = (-3/5)(5) + b. Solving for b, we get b = -5 + 3 = -2. Therefore, the equation for the line is y = (-3/5)x - 2.

Explanation
The equation for a line running through two points, A(2, 1) and B(-2, -7), can be found using the slope-intercept form of a linear equation, y = mx + b. The slope, m, can be calculated using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, we get m = (-7 - 1) / (-2 - 2) = -8 / -4 = 2. Next, we can substitute the slope and one of the points into the equation to find the y-intercept, b. Using point A(2, 1), we get 1 = 2(2) + b, which simplifies to b = -3. Therefore, the equation for the line is y = 2x - 3.

Explanation
To find the equation of a line parallel to another line, we need to use the same slope. The slope of the given line can be found using the formula (y2 - y1) / (x2 - x1), which gives us (-5 - 3) / (-2 - 4) = -8 / -6 = 4/3. Since the parallel line also passes through the point (-2, 1), we can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Plugging in the values, we get y - 1 = (4/3)(x - (-2)), which simplifies to y - 1 = (4/3)(x + 2).

Explanation
The equation for a line can be determined using the 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 line k, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Plugging in the coordinates of the given points, we have (2 - (-4)) / (-1 - 3) = 6 / (-4) = -3/2.

Since line l is perpendicular to line k, the slope of line l is the negative reciprocal of the slope of line k, which is 2/3.

Now, we can use the slope-intercept form and the coordinates of a point on line l to find the equation. Plugging in the coordinates of (-4, -3), we have -3 = (2/3)(-4) + b. Solving for b, we get b = -3 + 8/3 = -1/3.

Therefore, the equation for line l is y = (2/3)x - 1/3.

Explanation
The cost to be paid by the passenger is calculated by adding the cost for the first ride (b) to the cost per distance (a) multiplied by the distance traveled (x). In this case, the distance traveled is 6500 meters. So, the cost to be paid by Deni is 3000 + (20000 * 6500/100) = 16000. Therefore, the correct answer is Rp16.000,00.