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Find the equation of the line through the points (-3,3) and (3,5) using point-slope form. Then rewrite the equation in slope-intercept form.

User Edymerchk
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Given:

A line passes through the points (-3,3) and (3,5).

To find:

The equation of the line by using point slope form, then rewrite the equation in slope-intercept form.

Solution:

It is given that the line passes through the points (-3,3) and (3,5). So, the slope of the line is:


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


m=(5-3)/(3-(-3))


m=(2)/(6)


m=(1)/(3)

The point slope form of a line is:


y-y_1=m(x-x_1)

Where, m is the slope.

The point slope form of the given line is:


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


y-3=(1)/(3)(x+3)

The point slope form of the given line is
y-3=(1)/(3)(x+3).

We need to rewrite this equation in slope intercept form, i.e.,
y=mx+b, where m is slope and b is y-intercept.

The above equation can be rewritten as:


y-3=(1)/(3)(x)+(1)/(3)(3)


y-3=(1)/(3)(x)+1


y=(1)/(3)(x)+1+3


y=(1)/(3)(x)+4

Therefore, the slope intercept form of the given line is
y=(1)/(3)(x)+4.

User Cashif Ilyas
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