Question

Find an expression for the function whose graph is the given curve.The line segment joining the points (1,-3) and (5, 7).

Short answer

The expression for the function is\({\bf{y = }}\frac{{\bf{5}}}{{\bf{2}}}{\bf{x - }}\frac{{{\bf{11}}}}{{\bf{2}}}\).

Step-by-step solution

Determine the formula for the curve passing through two points

The equation of a line passing through the two points\(\left( {{x_1},{y_1}} \right)\)and\(\left( {{x_2},{y_2}} \right)\)is given as:

\(y - {y_1} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)\)

Determine the expression of the curve passing through two points

The given two points are\(\left( {1, - 3} \right)\)and\(\left( {5,7} \right)\).

Substitute all the values in the above equation.

\(\begin{array}{c}y - \left( { - 3} \right) = \frac{{7 - \left( { - 3} \right)}}{{5 - 1}}\left( {x - 1} \right)\\y + 3 = \frac{{10}}{4}\left( {x - 1} \right)\\y = \frac{5}{2}x - \frac{{11}}{2}\end{array}\)

Therefore, the expression for the function is\(y = \frac{5}{2}x - \frac{{11}}{2}\).