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Write an equation for the line that passes through (3,5) and (9,9) in point slope form

Sagot :

amysun2025

Answer:

[tex]y-5=\frac{2}{3}(x-3)[/tex]

Step-by-step explanation:

Hi there!

We are given the points (3,5) and (9,9) and we want to write the equation of the line that contains those two points in point-slope form

Point-slope form is written as [tex]y-y_1=m(x-x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point and m is the slope

First, let's find the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We are given two points, but let's label their values to avoid confusion and mistakes when calculating:
[tex]x_1=3\\y_1=5\\x_2=9\\y_2=9[/tex]
Now substitute these points into the formula; remember that m is the value of the slope.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:

m=[tex]\frac{9-5}{9-3}[/tex]
Subtract

m=[tex]\frac{4}{6}[/tex]

Simplify the fraction

m=[tex]\frac{2}{3}[/tex]

Now that we have the value of m (slope), and also the values of [tex]x_1[/tex] and [tex]y_1[/tex] (the points), let's substitute these values into the formula for point-slope form.

[tex]y-y_1=m(x-x_1)[/tex]
[tex]m=\frac{2}{3}, x_1=3, y_1=5[/tex]
Substitute these values into the formula

[tex]y-5=\frac{2}{3}(x-3)[/tex]

Hope this helps!

If you would like a similar problem for practice, here is one for you: https://brainly.com/question/24217374

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