Question

If a line contains the points shown in the table, the equation of the line, in slope-intercept form, is х -8 -3 0 6у –42 -17 -2 28

Answer 1

The slope-intercept form of the equation of a line, is:

`y=mx+b`

Where m, the coefficient of x, is the slope of the line, and b, the constant term, is the y-intercept.

To find the slope of the line, substitute the corresponding values of x and y into the slope formula. Use, for instance, the points (-8,-42) and (6,28):

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=((28)-(-42))/((6)-(-8)) \\ =(28+42)/(6+8) \\ =(70)/(14) \\ =5 \end{gathered}`

The y-intercept equals the value of y when x=0. From the table, we can see that the y-intercept is equal to -2.

Substitute m=5 and b=-2 to find the equation of the line described by the table.

Therefore, requested the equation in slope-intercept form, is:

`y=5x-2`