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How do you write an equation in standard form for a line passing through(–2, 1) and (4, 13)?

Answer 1

Nathan Axel

The equation is : #y = 2x + 5#

Any linear function has the following form : #y = mx + b#

Firstly, you need to find the slope #m# of your line.

It is given by :

#m = (y_2-y_1)/(x_2-x_1)#,

where #(x_1,y_1)=(-2,1)# and #(x_2,y_2) = (4,13)# or vice versa.

So #m = (13-1)/(4+2) = 2#.

Then, in order to find #b#, you have to solve the following equation :

#y_1 = mx_1 + b# or #y_2 = mx_2 + b#

So #1 = 2*(-2) + b => b = 5#

Now you have the equation of your line :

#y = 2x + 5#

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Answer 2

Jameson Allen

To write the equation of a line in standard form given two points, you first find the slope using the formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} ). Then, substitute the slope and one of the given points into the point-slope form: ( y - y_1 = m(x - x_1) ). After that, you simplify the equation and rewrite it in standard form: ( Ax + By = C ), where ( A ), ( B ), and ( C ) are integers, and ( A ) is positive.

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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.