Final answer:
To identify the equation of a line passing through given points, one must first calculate the slope using the difference in y-values divided by the difference in x-values. After calculating the slope, the y-intercept can be determined by substituting the slope and one of the points into the slope-intercept form of a linear equation. However, the results do not match any of the available options, suggesting a possible error or typo in the choices or question.
Step-by-step explanation:
The student has asked to determine which linear equation represents a line passing through the roots (-7,0) and (-13,0), and crossing the point (-10,3). First, let us establish the slope of the line by using the two given roots. The slope (m) can be calculated by the formula m = (y2 - y1) / (x2 - x1). In our case, since both points have y-coordinates of 0, the slope is 0. This means our line is horizontal and will not pass through the point (-10,3) which has a y-coordinate of 3. However, there might be an error in the premise since horizontal lines do not have points with different y-coordinates. Therefore, let's calculate the slope again using the points (-7,0) and (-10,3).
m = (3 - 0) / (-10 + 7) = 3 / -3 = -1
Now that we have the slope, we use one of the points to find the y-intercept (b). Let's use the point (-10,3). Using the slope-intercept form of a linear equation (y = mx + b), we substitute m with -1, and x and y with -10 and 3, respectively:
3 = (-1)(-10) + b
b = 3 - 10
b = -7
Now we can write the equation of the line as y = -1x - 7. However, this equation is not one of the options provided. We must have made an error in our calculations or the choices given may have a typo. Since neither choice matches, we'll need more information or clarification to provide a correct answer.