Write an equation in slope-intercept form of the line that passes through the given points \left[\begin{array}{ccc}x&y\\-4&9\\-2&4\\0&-1\\2&-6\end{array}\rig…

Question

Write an equation in slope-intercept form of the line that passes through the given points


`\left[\begin{array}{ccc}x&y\\-4&9\\-2&4\\0&-1\\2&-6\end{array}\right]`

Answer 1

y = -
`(5)/(2)` x - 1

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table

m =
`(-6-9)/(2-(-4))` =
`(-15)/(2+4)` =
`(-15)/(6)` = -
`(5)/(2)`

the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then

c = - 1

y = -
`(5)/(2)` x - 1 ← equation of line