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.

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:

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:

  ---- (1)

Equation (1) requires two point  and 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.

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