Example Question - y-intercept determination
Here are examples of questions we've helped users solve.
Determining Equation of Trend Line in Scatter Plot with Two Points
To determine the equation of the trend line in a scatter plot, you usually need two points on the line to find the slope and then use one of these points to solve for the y-intercept. From the image provided, we can identify two points on the trend line. Let's select two points that clearly lie on the line and are easy to read: Point 1 (on the left end of the line): It looks like it crosses the y-axis at y = 1. This would make the point (0,1). Point 2 (somewhere on the line where it crosses a grid intersection): It's hard to tell exactly from this image, but let's assume it's (5,5). Next, we calculate the slope (m) using the formula: \( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \) Plugging in the point values: \( m = \frac{(5 - 1)}{(5 - 0)} \) \( m = \frac{4}{5} = 0.8 \) With the slope of 0.8 and knowing the line crosses the y-axis at (0,1), we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the trend line is: y = 0.8x + 1 Please note that the accuracy of this equation depends on how precisely we can read the points from the image. For a more accurate equation, a clear reading of exact points on the line or the actual data used to generate the scatter plot would be necessary.
Determining Equation of Trend Line on Scatter Plot
To determine the equation of the trend line on a scatter plot, we typically look for two points through which the line passes. Once we have those points, we can use them to calculate the slope of the line and then use one of the points to find the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. From the image, it's not possible to determine the exact coordinates of the points on the trend line with absolute precision, but we can estimate based on the grid. Let's identify two points that the trend line appears to pass through. For example, one point on the trend line seems to be approximately at (1, 1). The other point that we can infer intersects the trend line and grid line might be at (10, 9). Let's use these two estimated points to calculate the slope (m). The slope is calculated by taking the difference in the y-values divided by the difference in the x-values: \( m = (y_2 - y_1) / (x_2 - x_1) \) Using our estimated points (1, 1) and (10, 9): \( m = (9 - 1) / (10 - 1) \) \( m = 8 / 9 \) Now that we know the slope, we can determine the y-intercept (b) of the trend line using the y = mx + b format and one of the points. Let's use point (1, 1): \( y = mx + b \) \( 1 = (8/9)(1) + b \) \( b = 1 - 8/9 \) \( b = 1/9 \) So, the equation of the trend line, based on our estimations, would be approximately: \( y = (8/9)x + 1/9 \) Keep in mind that since the exact coordinates of the points the trend line passes through are not clearly provided, the equation obtained is based on visual estimation and might not be the precise equation used to generate the trend line in the scatter plot. However, without more accurate data, this is the best estimation we can make based on the provided image.
Analyzing a Linear Relationship on a Cartesian Coordinate Plane
The image depicts a Cartesian coordinate plane with an x-axis and a y-axis. There is a straight line graphed that passes through the origin (0,0) and extends into the first quadrant, indicating a positive linear relationship between x and y. Additionally, there is a red dot marked on the line. To solve a question related to this graph, I would need to know the specific question you have in mind, as there could be several questions related to finding the equation of the line, calculating the slope, determining the y-intercept, or interpreting the significance of the point marked with the red dot. However, based on the common tasks associated with such graphs, I can provide a general overview: 1. To find the slope of the line, you could pick two points on the line, find the change in y (rise) over the change in x (run), and use the slope formula: slope (m) = rise / run. 2. Since the line passes through the origin, it's clear that the y-intercept is 0, so the equation of the line would be in the form of y = mx. 3. If the question is about the red dot, we would need to determine its coordinates. Unfortunately, I can't measure the precise location on this image, so you would have to provide the coordinates or the context around what is needed regarding that point. Please provide the specific question or details regarding what you need to solve using this graph, and I'll be glad to assist further.
Finding Linear Function through Two Points
To determine the linear function that goes through the points (3, -9) and (5, 13), we will use the slope-intercept form of a line, which is y = mx + b. Here, 'm' is the slope and 'b' is the y-intercept. First, calculate the slope (m) using the two points: m = (y2 - y1) / (x2 - x1) = (13 - (-9)) / (5 - 3) = 22 / 2 = 11 Now we have the slope, which is 11. Next, we use one of the points to find the y-intercept (b). Let's use point (3, -9) and substitute x and y into the equation along with our slope: -9 = 11 * 3 + b -9 = 33 + b b = -9 - 33 b = -42 Our linear function is y = 11x - 42.
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