Question

Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-interceptform.x1520253035HHHу160200240280320An equation of the line in point-slope form is

Answer 1

Point slope form: y - 160 = 8(x-15)

Slope intercept form: y = 8x + 40

Step-by-step explanation:

To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y

Points chosen: (20, 200) and (15, 160)

m = slope = (change in y)/ (change in x)

`\begin{gathered} m\text{ = }(200-160)/(20-15)\text{ = }(40)/(5) \\ m\text{ = 8} \end{gathered}`

Point-slope form:

`\begin{gathered} y-y_1=m(x-x_1)\text{ then we would pick any of the points used earlier} \\ U\sin g\text{ (15, 160)} \\ y\text{ - 160 = 8( x - 15)} \\ y\text{ - 160 = 8x -120} \\ y\text{ =}8x\text{ + 40} \end{gathered}`

The equation in the slope intercept form:

`\begin{gathered} y\text{ = mx + b} \\ y\text{ = 8x + 40} \\ \text{where m = 8 b = intercept = 40} \end{gathered}`

Hence, Point slope form: y - 160 = 8(x-15)

Slope intercept form: y = 8x + 40