What is an equation in point-slope form for the line that passes through the points (-1, 4) and (2, -2)?
To find the equation of a line in point-slope form, you need to know the slope of the line and one point it passes through.
First, let's find the slope of the line using the formula:
slope = (change in y)/(change in x)
In this case, we'll use the coordinates (-1, 4) and (2, -2) to calculate the slope.
change in y = -2 - 4 = -6
change in x = 2 - (-1) = 3
slope = -6/3 = -2
Now that we have the slope (-2) and one point the line passes through (-1, 4), we can use the point-slope form of the equation which is:
y - y1 = m(x - x1)
Let's substitute the values we have:
y - 4 = -2(x - (-1))
Simplifying further:
y - 4 = -2(x + 1)
y - 4 = -2x - 2
To convert it to the standard form, let's bring all terms to the left side:
2x + y = -2 - 4
2x + y = -6
Thus, the equation in point-slope form for the line passing through the points (-1, 4) and (2, -2) is 2x + y = -6.