Question

A student created this table to represent a linear relationship between x and y.X Y-2. 10.0-1. 7.50. 5.01. 2.52. 0 Part AWhat is the y-intercept of the line represented by the x and y values shownin the table? Show or explain how you got your answer.Enter your answer and your work or explanation in the space provided.

Answer 1

To find the equation of the line, we pick two corresponding points of x and y,

$\begin{gathered} (x_1,y_1)=(0,5.0) \\ (x_2,y_2)=(2,0) \end{gathered}$

Formula to find the equation of a line is,

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the points into the formula to find the equation of a line above,

$\begin{gathered} \frac{y-5}{x-0}=\frac{0-5}{2-0} \\ \text{Crossmultiply} \\ 2(y-5)=-5(x) \\ \text{Open bracket} \\ 2y-10=-5x \\ 2y=-5x+10 \\ \text{Divide both sides by 2} \\ \frac{2y}{2}=\frac{(-5x+10)}{2} \\ y=-\frac{5}{2}x+5 \end{gathered}$

Where the general equation of a straight line is given as,

$\begin{gathered} y=mx+c \\ \text{Where m is the slope and c is the y-intercept} \end{gathered}$$\begin{gathered} \text{The equation of the line is,} \\ y=-\frac{5}{2}x+5 \end{gathered}$

Comparing both equations, the c = 5, is the y-intercept.

Alternatively,

The y-intercept is the point where x = 0 and from the table provided,

Where x = 0, y = 5.

Hence, the y-intercept is 5.