How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

1 Answer
Dec 20, 2016

Answer:

#y = 5/2x + 41/2#

Explanation:

First, build the equation using the information given, the slope and a point, using the point-slope formula.

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))#
Where #color(red)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the information from the problem gives the equation:

#y - 3 = 5/2(x - -7)#

#y - 3 = 5/2(x + 7)#

The slope-intercept for of a linear equation is #color(red)(y = mx + b)# where #color(red)(m)# is the slope and #color(red)(b)# is the y-intercept.

To transform our equation we must solve for #y# while keeping the equation balanced:

#y - 3 = 5/2x + (5/2 xx 7)#

#y - 3 = 5/2x + 35/2#

#y - 3 + color(red)(3) = 5/2x + 35/2 + color(red)(3)#

#y - 0 = 5/2x + 35/2 + (3 xx 2/2)#

#y = 5/2x + 35/2 + 6/2#

#y = 5/2x + (35 + 6)/2#

#y = 5/2x + 41/2#