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.
Accepted Solution
A:
Helena is correct in saying that the point-slope form will generate the equation. The point-slope form is written as:
y-yβ = m(x-xβ), where, m = (yβ-yβ)/(xβ-xβ) is the slope of the line (xβ,yβ) and (xβ,yβ) 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.Β 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.