Question

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.

Answer 1

Answer: $(y+5)=\frac{5}{7}(x-8)$

Step-by-step explanation:

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

$(y-b)=m(x-a)$

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

The slope of the line =$\frac{5}{7}$

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

$(y-(-5))=\frac{5}{7}(x-8)\\\\\Rightarrow\ (y+5)=\frac{5}{7}(x-8)$

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

Answer 2

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

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

$y-b=m(x-a).$

For the given line, we have

$m=\dfrac{5}{7},~~~(a,b)=(8,-5).$

Therefore, the equation of the line will be

$y-b=m(x-a)\\\\\Rightarrow y-(-5)=\dfrac{5}{7}(x-8)\\\\\Rightarrow y+5=\dfrac{5}{7}(x-8).$

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