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What is the point-slope form of a line with slope [tex]\frac{4}{5}[/tex] that contains the point [tex]\((-2,1)\)[/tex]?

A. [tex]y+1=\frac{4}{5}(x-2)[/tex]
B. [tex]y+1=\frac{4}{5}(x+2)[/tex]
C. [tex]y-1=\frac{4}{5}(x+2)[/tex]
D. [tex]y-1=\frac{4}{5}(x-2)[/tex]


Sagot :

Sure, let's find the point-slope form of the equation for a line that has a slope of [tex]\(\frac{4}{5}\)[/tex] and passes through the point [tex]\((-2, 1)\)[/tex].

The point-slope form of the equation of a line is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\( m \)[/tex] is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.

Here, the slope [tex]\( m \)[/tex] is [tex]\(\frac{4}{5}\)[/tex], and the point [tex]\((x_1, y_1)\)[/tex] is [tex]\((-2, 1)\)[/tex].

Let's substitute the given values into the point-slope form equation:

[tex]\[ y - 1 = \frac{4}{5}(x - (-2)) \][/tex]

Simplify the expression inside the parentheses:

[tex]\[ y - 1 = \frac{4}{5}(x + 2) \][/tex]

So, the point-slope form of the line is:

[tex]\[ y - 1 = \frac{4}{5}(x + 2) \][/tex]

Now, let's compare this with the given options:

A. [tex]\( y + 1 = \frac{4}{5}(x - 2) \)[/tex]

B. [tex]\( y + 1 = \frac{4}{5}(x + 2) \)[/tex]

C. [tex]\( y - 1 = \frac{4}{5}(x + 2) \)[/tex]

D. [tex]\( y - 1 = \frac{4}{5}(x - 2) \)[/tex]

The correct equation from our calculation is [tex]\( y - 1 = \frac{4}{5}(x + 2) \)[/tex], which matches option:

C. [tex]\( y - 1 = \frac{4}{5}(x + 2) \)[/tex]

Thus, the correct answer is:

C. [tex]\( y - 1 = \frac{4}{5}(x + 2) \)[/tex]