Question

How do you write the equation in slope intercept form given (-5,6) (4,4)?

Answer 1

`color(brown)(y = (-2/9)x + 35/9, Slope = -2/9, "y-intercept " = 35/9`

Explanation:

Slope intercept form of equation is `y = m x + c`

where m is the slope and c is the y-intercept.

Equation of a line is given by the formula,

`(y-y_1) / (y_2-y_1) = (x - x_1) / (x_2 - x_1), " knowing the two points on the line"`

`"Given : (x_1,y_1) = -5,6), (x_2, y_2) = (4,4)`

`:.(y - 6) / (4 - 6) = (x + 5) / (4 + 5)`

`(y - 6) / -2 = (x+5) / 9`

`y - 5 = (-2/9)x - -10/9`

`y = (-2/9) x - 10 / 9 + 5`

`color(brown)(y = (-2/9)x + 35/9, Slope " " = m = -2/9, "y-intercept "= c = 35/9`