How do you write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5),?

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Answer 1 · 2017-01-25T14:49:48

#y = color(red)(-3)x + color(blue)(5)#

First, we must find the slope.

The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(5) - color(blue)(-7))/(color(red)(0) - color(blue)(4))#

#m = (color(red)(5) + color(blue)(7))/(color(red)(0) - color(blue)(4))#

#m = 12/-4#

#m = -3#

The second point in the problem gives us the y-intercept = #color(blue)(5)#

The slope-intercept form of a linear equation is:

#y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Substituting the slope and the y-intercept gives:

#y = color(red)(-3)x + color(blue)(5)#