Example Question - points on a line
Here are examples of questions we've helped users solve.
Solving for a Variable with Given Coordinates
To solve for \( n \), we need to use the given information about the coordinates of the points on the line. The coordinates of the two points are given as \( P_1(-18, 18) \) and \( P_2(2, n) \). The slope \( m \) of a line passing through two points \( P_1(x_1, y_1) \) and \( P_2(x_2, y_2) \) can be found using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Given that the slope is 0 (from the information provided about the equation of the line), this means that the line is horizontal and there is no change in the y-values between points \( P_1 \) and \( P_2 \). Therefore, \( y_1 = y_2 \), or equivalently, \( 18 = n \). So, the value of \( n \) is 18.
Finding the Value of n to Form a Straight Line
The question seems to be in reference to finding the value of \(n\) so that the points mentioned form a straight line. The points given are (9, 18) and (4, \(n\)). To find the value of \(n\), we can use the concept of slope, which should be consistent for all points on a straight line. The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] If the points (9, 18) and (4, \(n\)) are on the same line, they must have the same slope. As we do not have another point to compare, let's assume that these two points should form a line with a slope that we can calculate. Using our known points: \[ m = \frac{18 - n}{9 - 4} \] \[ m = \frac{18 - n}{5} \] If you have another point or a given slope, you could solve for \(n\) by setting up the equation with the slope (or the third point) given. However, without additional information, we cannot determine the specific value of \(n\), because any point (4, \(n\)) will still form a line with the point (9, 18) regardless of the value of \(n\), just that the slope will be different. So with only the information provided in the image, we cannot find a specific value for \(n\). We would need the slope of the line or a third point to solve for \(n\).
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