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. make the writing short

Answer 1

Both Samuel and Helena are correct; either form can be used to find the equation of a line given two points.

Slope-Intercept Form: This form is represented as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. To use this form, you first calculate the slope using the two points and then solve for \( b \) to find the equation.

Point-Slope Form: This form is expressed as \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is one of the points and \( m \) is the slope. This method is direct and keeps the specific points in focus, making it easy to write the equation without needing the y-intercept.

In summary, both methods effectively yield the same final equation of the line, so either one is valid.