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A line contains the point (8, –5). If the slope of the line is 5/7, write the equation of the line using point-slope form.

Respuesta :

JeanaShupp

Answer: [tex](y+5)=\frac{5}{7}(x-8)[/tex]

Step-by-step explanation:

The point slope form of a line having slope m and point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given: A line contains the point = (8, –5)

The slope of the line =[tex]\frac{5}{7}[/tex]

Now, the point slope form of a line having slope [tex]\frac{5}{7}[/tex] and point (8,-5) is given by :-

[tex](y-(-5))=\frac{5}{7}(x-8)\\\\\Rightarrow\ (y+5)=\frac{5}{7}(x-8)[/tex]

Hence, the equation of the line =[tex](y+5)=\frac{5}{7}(x-8)[/tex]

Answer:  The required equation of the line is [tex]y+5=\dfrac{5}{7}(x-8).[/tex]

Step-by-step explanation:  Given that a line contains the point (8, -5) and the slope of the line is {tex]\dfrac{5}{7}.[/tex]

We are to write the equation of the line using point-slope form.

We know that

the equation of a line with slope m and passing through the point (a, b) is given by

[tex]y-b=m(x-a).[/tex]

For the given line, we have

[tex]m=\dfrac{5}{7},~~~(a,b)=(8,-5).[/tex]

Therefore, the equation of the line will be

[tex]y-b=m(x-a)\\\\\Rightarrow y-(-5)=\dfrac{5}{7}(x-8)\\\\\Rightarrow y+5=\dfrac{5}{7}(x-8).[/tex]

Thus, the required equation of the line is [tex]y+5=\dfrac{5}{7}(x-8).[/tex]