Jaystar456
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The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

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MissPhiladelphia

Helena is correct in saying that the point-slope form will generate the equation. The point-slope form is written as:


y-y₁ = m(x-x₁), where,

m = (y₂-y₁)/(x₂-x₁) is the slope of the line

(x₁,y₁) and (x₂,y₂) are the coordinates of the two points


On the other hand, the slope-intercept form is written as:


y = mx + b, where,

m is the slope of the line

b is the y-intercept


In this case, since only two points were given, the y-intercept of the line is not readily known. Thus, it is only through the point-slope form that the equation of the line can be determined. This is because it only requires the substitution of the x and y-coordinates of the points in the equation. 

Halena claims that point slope form will find the equation of a line therefore,  she is correct because two points are given in the question and point slope form requires two point to determine the equation of a line.

Given :

Two points are given.

The slope intercept form is given by the equation:

[tex]y = mx+c[/tex]

The above equation requires a slope m of the line and the intercept c to determine the equation of a line.

The point slope form is giveen by the equation:

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]   ---- (1)

Equation (1) requires two point [tex](x_1,y_1)[/tex]  and [tex](x_2,y_2)[/tex] to determine the equation of a line.

Therefore, Halena is correct because two points are given in the question and point slope form requires two point to determine the equation of a line.

For more information, refer the link given below:

https://brainly.com/question/19214360

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