Write an equation of the line that passes through the given points.
(-1,7) and (2,-5)
To find the equation of the line that passes through the given points (-1,7) and (2,-5), we first need to find the slope of the line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given values (-1,7) and (2,-5) into the formula, we have:
m = (-5 - 7) / (2 - (-1))
m = (-12) / (2 + 1)
m = -12 / 3
m = -4
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Substituting one of the given points (-1,7) into the equation, we have:
y - 7 = -4(x - (-1))
y - 7 = -4(x + 1)
y - 7 = -4x - 4
Rearranging the equation to the standard form (Ax + By = C), we have:
4x + y = 3
Therefore, the equation of the line that passes through the given points (-1,7) and (2,-5) is 4x + y = 3.