Final answer:
The slope of the line passing through points (-5, 15) and (-10, 18) is -3/5. The point-slope form of the line is y - 15 = -3/5(x + 5).
Step-by-step explanation:
The question asks us to determine the point-slope form of a line that passes through two given points and to find the slope of that line. The two points provided are (-5, 15) and (-10, 18).
To find the slope of the line, we use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points into the formula, we get:
m = (18 - 15) / (-10 - (-5))
m = 3 / (-5)
m = -3/5
The slope of the line is -3/5, which means for every increase of 5 units in the x direction, there is a decrease of 3 units in the y direction.
To write the equation in point-slope form, we use the formula y - y1 = m(x - x1). Using one of the given points (-5, 15) and the slope m = -3/5, we can write the point-slope form as:
y - 15 = -3/5(x + 5)
This is the point-slope form of the line that passes through the points (-5, 15) and (-10, 18).