Persamaan Garis Lurus (Kls.8)

1) Gradien garis yang melalui titik (2, 1) dan (4,7) adalah ... .

2

3

The gradient of a line is calculated by finding the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the change in y-coordinates is 7 - 1 = 6, and the change in x-coordinates is 4 - 2 = 2. Therefore, the gradient is 6/2 = 3.

Explanation

The gradient of a line is calculated by finding the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the change in y-coordinates is 7 - 1 = 6, and the change in x-coordinates is 4 - 2 = 2. Therefore, the gradient is 6/2 = 3.

2) Persamaan garis lurus yang melalui titik (2, 1) dan (-2, -7) adalah ... .

y = -2x + 5

y = 2x - 3

y = 3x - 5

y = -3x + 7

The equation of a straight line passing through two points (x1, y1) and (x2, y2) can be found using the formula: y - y1 = (y2 - y1) / (x2 - x1) * (x - x1). In this case, the points are (2, 1) and (-2, -7). Plugging in these values into the formula, we get: y - 1 = (1 - (-7)) / (2 - (-2)) * (x - 2). Simplifying the equation gives us y - 1 = 8/4 * (x - 2), which further simplifies to y - 1 = 2(x - 2). Rearranging the equation gives us y = 2x - 3, which matches the given answer.

Explanation

The equation of a straight line passing through two points (x1, y1) and (x2, y2) can be found using the formula: y - y1 = (y2 - y1) / (x2 - x1) * (x - x1). In this case, the points are (2, 1) and (-2, -7). Plugging in these values into the formula, we get: y - 1 = (1 - (-7)) / (2 - (-2)) * (x - 2). Simplifying the equation gives us y - 1 = 8/4 * (x - 2), which further simplifies to y - 1 = 2(x - 2). Rearranging the equation gives us y = 2x - 3, which matches the given answer.

3) Gradien garis yang sejajar dengan garis 2x + 6y + 8 = 0 adalah ... .

Garis yang sejajar dengan garis 2x + 6y + 8 = 0 akan memiliki gradien yang sama. Dalam persamaan garis umum Ax + By + C = 0, gradien garis dapat ditemukan dengan membagi koefisien x dengan koefisien y, yaitu -A/B. Dalam hal ini, gradien garis sejajar dengan 2x + 6y + 8 = 0 adalah -2/6 atau -1/3.

Explanation

Garis yang sejajar dengan garis 2x + 6y + 8 = 0 akan memiliki gradien yang sama. Dalam persamaan garis umum Ax + By + C = 0, gradien garis dapat ditemukan dengan membagi koefisien x dengan koefisien y, yaitu -A/B. Dalam hal ini, gradien garis sejajar dengan 2x + 6y + 8 = 0 adalah -2/6 atau -1/3.

4) Garis p tegak lurus terhadap garis h yang mempunyai persamaan 3x + 6y + 5 = 0. Gradien garis p adalah ... .

-2

2

The gradient of a line perpendicular to another line is the negative reciprocal of the gradient of that line. The given line has the equation 3x + 6y + 5 = 0. To find the gradient of this line, we can rearrange the equation into the slope-intercept form y = mx + c, where m is the gradient. By rearranging the equation, we get y = (-1/2)x - 5/6. Therefore, the gradient of the given line is -1/2. The negative reciprocal of -1/2 is 2. Therefore, the gradient of the line p perpendicular to the given line is 2.

Explanation

The gradient of a line perpendicular to another line is the negative reciprocal of the gradient of that line. The given line has the equation 3x + 6y + 5 = 0. To find the gradient of this line, we can rearrange the equation into the slope-intercept form y = mx + c, where m is the gradient. By rearranging the equation, we get y = (-1/2)x - 5/6. Therefore, the gradient of the given line is -1/2. The negative reciprocal of -1/2 is 2. Therefore, the gradient of the line p perpendicular to the given line is 2.

5) Persamaan garis yang tegak lurus terhadap sumbu x adalah ... .

x = y

y = 0

x - 3 = 0

y - 2x = 0

The equation x - 3 = 0 represents a line that is perpendicular to the x-axis. This is because the equation is in the form of x = constant, which means that the line is parallel to the y-axis. Since the y-axis is perpendicular to the x-axis, any line parallel to the y-axis will be perpendicular to the x-axis. Therefore, the equation x - 3 = 0 represents a line that is perpendicular to the x-axis.

Explanation

The equation x - 3 = 0 represents a line that is perpendicular to the x-axis. This is because the equation is in the form of x = constant, which means that the line is parallel to the y-axis. Since the y-axis is perpendicular to the x-axis, any line parallel to the y-axis will be perpendicular to the x-axis. Therefore, the equation x - 3 = 0 represents a line that is perpendicular to the x-axis.

6) Gradien garis 3x + 5y - 6 = 0 adalah ... .

The gradient of the line 3x + 5y - 6 = 0 is -3/5.

Explanation

The gradient of the line 3x + 5y - 6 = 0 is -3/5.

7) Persamaan garis yang sejajar dengan garis yang melalui titik-titik (-3, 4) dan (2, -1) adalah ... .

2x + y = 4

x - y = 4

x + y = 4

-x - y = 4

The equation of a line parallel to a given line will have the same slope. The slope of the line passing through the points (-3, 4) and (2, -1) can be found using the formula (y2 - y1) / (x2 - x1). Plugging in the values, we get (-1 - 4) / (2 - (-3)) = -5 / 5 = -1. Therefore, the slope of the line is -1. The equation x - y = 4 has a slope of 1, which is the negative reciprocal of -1. So, this equation represents a line parallel to the line passing through the given points.

Explanation

The equation of a line parallel to a given line will have the same slope. The slope of the line passing through the points (-3, 4) and (2, -1) can be found using the formula (y2 - y1) / (x2 - x1). Plugging in the values, we get (-1 - 4) / (2 - (-3)) = -5 / 5 = -1. Therefore, the slope of the line is -1. The equation x - y = 4 has a slope of 1, which is the negative reciprocal of -1. So, this equation represents a line parallel to the line passing through the given points.