What method can be used to write the equation of a line in slope-intercept form given two points?

Solution:

The equation of a line in slope-intercept form is given by 

y = mx + c

When two points are given, we can find the slope of the line using the formula

\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=m\)

Now, use any one of the given points and slope to formulate the equation of a line.

The equation of a line when one point and slope is given can be written using the formula

\((y -y_{1}) = m(x-x_{1})\)

For example, let two points be (1,3) and (4,9)

Now, find slope

m = (9 - 3) / (4 - 1)

m = 6 / 3

m = 2

Use point (1,3) and slope 2 to find the equation of the line

(y - 3) = 2(x - 1)

y - 3 = 2x - 2

y = 2x - 2 + 3

y = 2x + 1

Therefore, the equation of the line is y = 2x + 1.

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What method can be used to write the equation of a line in slope-intercept form given two points?

Summary:

When two points are given, the equation of a line in slope-intercept form can be found by using 

\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=m\) and \((y -y_{1})=m(x-x_{1})\).