Question

See attachment for graph. Write an equation in slope intercept form for the graph. Then tell what the slope and y-intercept represent.Equation; Slope (in words):Y intercept (in words):

Answer 1

From the graph, the coordinates given are

`\begin{gathered} (x_1,y_1)\Rightarrow(0,50) \\ (x_2,y_2)\Rightarrow(3,350) \end{gathered}`

The general equation of a line in slope-intercept form is

`\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \\ c=y-\text{intercept} \end{gathered}`

The formula used to calculate the equation of a line when two points (x1,y1) and (x2,y2) are given is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

By substituting the values, we will have

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (y-50)/(x-0)=(350-50)/(3-0) \\ (y-50)/(x)=(300)/(3) \\ (y-50)/(x)=100 \\ \text{cross multiply} \\ y-50=100x \\ y=100x+50 \end{gathered}`

Therefore,

The equation of the line is y = 100x + 50

By comparing coefficients,

The slope = 100 ( one hundred dollars balance per deposit)

The y-intercept = 50 ( fifty dollars)