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How do you write an equation in standard form of the lines passing through (2,1) (4,5)?

Answer 1

Julia Adams

#color(purple)(2x - y = 3 " is the standard form of equation"#

#(x_1, y_1) = (2,1), (x_2, y_2) = (4,5)#

Equation of a line passing through given two points is

#color(crimson)((y-y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1)#

#(y - 1) / (5-1) = (x - 2) / (4-2)#

#2 * (y - 1) = 4 * (x - 2)#

#2y - 2 = 4x - 8#

#4x - 2y = 6#

#color(purple)(2x - y = 3 " is the standard form of equation"#

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Answer 2

Savannah Anderson

To write an equation in standard form for the line passing through the points (2,1) and (4,5), you first find the slope using the formula: ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ). Then, you substitute the slope and one of the given points into the point-slope form equation ( y - y_1 = m(x - x_1) ). Finally, rearrange the equation to standard form: ( Ax + By = C ), where A, B, and C are integers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.