7. Write an equation of a line, in point-slope form, that passes through the two given
points.
Points: (-2, 3), (3, -1)
To find the equation of a line in point-slope form, we first need to find the slope of the line and then use one of the given points to write the equation.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (-2, 3) and (3, -1), we can find the slope:
m = (-1 - 3)/(3 - (-2))
m = (-4)/(3 + 2)
m = -4/5
Now that we have the slope of -4/5, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Using the point (-2, 3) as (x1, y1):
y - 3 = (-4/5)(x - (-2))
y - 3 = (-4/5)(x + 2)
y - 3 = (-4/5)x - 8/5
Therefore, the equation of the line in point-slope form that passes through the points (-2, 3) and (3, -1) is:
y - 3 = (-4/5)x - 8/5