To find the equation of a line that goes through the points (-2,3) and (3,-1), we can use either the point-slope form or the slope-intercept form.
First, let's find the slope of the line using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using the points (-2,3) and (3,-1), we have:
m = (-1 - 3) / (3 - (-2))
m = -4 / 5
So the slope of the line is -4/5.
Now, let's use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Using the point (-2,3) and the slope -4/5, we have:
y - 3 = -4/5(x - (-2))
y - 3 = -4/5(x + 2)
Expanding and simplifying:
y - 3 = -4/5x - 8/5
To convert the equation into slope-intercept form (y = mx + b), we need to isolate y:
y = -4/5x - 8/5 + 3
y = -4/5x - 8/5 + 15/5
y = -4/5x + 7/5
Therefore, a possible equation of the line in point-slope form is y - 3 = -4/5(x + 2) and in slope-intercept form is y = -4/5x + 7/5.
It's important to note that there are infinitely many equations that can describe a line passing through two points, as long as they have the same slope. The equations provided here are just one possible solution.