To find the equation of the line passing through the points (2, -1) and (6, 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)
Substitute the given points into the formula:
m = (5 - (-1)) / (6 - 2)
m = (5 + 1) / 4
m = 6 / 4
m = 3/2
Now, we have the slope of the line. To find the equation in point-slope form, we can choose one of the given points, for example (2, -1), and use the formula:
y - y1 = m(x - x1)
Substitute the slope and the point (2, -1) into the formula:
y - (-1) = (3/2)(x - 2)
y + 1 = (3/2)x - 3
y = (3/2)x - 4
Finally, we can write the equation in standard form:
2y = 3x - 8
Therefore, the equation of the line passing through (2, -1) and (6, 5) in standard form is 2y = 3x - 8.
an equation in standard form for the line that passes through (2.-1) and (6,5)
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