Final answer:
The equation of the line that passes through the points (-10, -7) and (-5, -9) is calculated by first determining the slope, which is -2/5, and then plugging this value along with one of the points into the point-slope form of a line equation, resulting in the final equation: y = (-2/5)x - 11.
Step-by-step explanation:
To find the equation of a line passing through two points, (-10, -7) and (-5, -9), we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). For the points given, this would be m = (-9 + 7) / (-5 + 10) = -2 / 5. The slope indicates that for every 5 units we move to the right along the x-axis, the line moves down by 2 units on the y-axis.
After finding the slope, we use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Choosing the point (-10, -7), our equation would become y + 7 = (-2/5)(x + 10). Simplify this to standard form to find the equation of the line.
In this instance, when we simplify the equation we get y + 7 = (-2/5)x - 4. Subtract 7 from both sides to get the final equation of the line: y = (-2/5)x - 11.