Final answer:
The points (-5, -25), (0, 0), and (3, 14) do not lie on the same straight line, so there is no single linear equation that represents all three. Thus, it's not possible to write a linear equation of the line passing through all three points.
Step-by-step explanation:
To find the equation of the line passing through the points (-5, -25), (0, 0), and (3, 14), we need to determine if these points fall on the same straight line. If they do, we can then calculate the slope (m) of the line using two of the points and use the point-slope form to write the equation.
Step 1: Check if Points Lie on the Same Line
Let's calculate the slope between the first two points (-5, -25) and (0, 0). The slope (m) is given by the difference in y-coordinates divided by the difference in x-coordinates, so m = (0 - (-25)) / (0 - (-5)) = 25 / 5 = 5.
Next, let's calculate the slope between the second and third points (0, 0) and (3, 14). Here, m = (14 - 0) / (3 - 0) = 14 / 3 which is not equal to 5, so the points do not fall on the same straight line and there is no single linear equation that passes through all three points.
Step 2: Finding the Equation (If Points Were Collinear)
If the points were collinear (lying on the same straight line), we would use the slope calculated from two points (we'll use (-5, -25) and (0, 0) for this example) to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the slope 5 and the point (0, 0), the equation would be:
y - 0 = 5(x - 0)
Therefore, the equation of the line would be y = 5x. However, since the points do not all lie on the same line, we cannot write a linear equation that fits all three.