Question

calculate the slope of the line. Use points that clearly cross the intersections of the graph paper B) write the equation for the line shown in the graph. Give your answer in slope intercept form Y=mx+b

Answer 1

A) In order to determine the slope of the line, use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

where (x1,y1) and (x2,y2) are two points on the line.

Based on the given graph, use the following points:

(x1,y1) = (-3,0)

(x2,y2) = (0,2)

Replace the previous values into the formula for m:

`m=(2-0)/(0-(-3))=(2)/(3)`

Hence, the slope of the line is 2/3.

B) To write the line equation, use the following general equation:

`y-y_0=m(x-x_0)`

Use (xo,yo) = (0,2) and m = 2/3 and solve for y:

`\begin{gathered} y-2=(2)/(3)\cdot(x-0) \\ y-2=(2)/(3)x \\ y=(2)/(3)x+2 \end{gathered}`

Hence, the equation of the line is y = 2/3 x + 2