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Sagot :
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:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{5-3}{3-(-3)}[/tex]
[tex]m=\dfrac{2}{6}[/tex]
[tex]m=\dfrac{1}{3}[/tex]
The point slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope.
The point slope form of the given line is:
[tex]y-3=\dfrac{1}{3}(x-(-3))[/tex]
[tex]y-3=\dfrac{1}{3}(x+3)[/tex]
The point slope form of the given line is [tex]y-3=\dfrac{1}{3}(x+3)[/tex].
We need to rewrite this equation in slope intercept form, i.e., [tex]y=mx+b[/tex], where m is slope and b is y-intercept.
The above equation can be rewritten as:
[tex]y-3=\dfrac{1}{3}(x)+\dfrac{1}{3}(3)[/tex]
[tex]y-3=\dfrac{1}{3}(x)+1[/tex]
[tex]y=\dfrac{1}{3}(x)+1+3[/tex]
[tex]y=\dfrac{1}{3}(x)+4[/tex]
Therefore, the slope intercept form of the given line is [tex]y=\dfrac{1}{3}(x)+4[/tex].
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