Sample Response: Both are correct. Using either form will result in the same equation. The slope-intercept form uses slope and a point to find the y-intercept. Point-slope form uses the slope and a point to solve for y to generate the equation.
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. 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.
