How do you find the x and y intercepts and slope if they exist and graph the line -2x + 7y = 14?

2 Answers
Jun 20, 2018

The x intercept is where #y=0# or #-2x=14# so is #x=-7.#

For the slope and y intercept we write #7y=2x+14# or #y=2/7 x + 2# and read off the slope of #2/7# and y intercept at #y=2.#

Jun 20, 2018

Answer:

#y# intercept: #(0,2)#

#x# intercept: #(-7,0)#

Slope: #2/7#

Explanation:

To find the intercepts, set one of the coordinates to zero and solve for the other:

#y# intercept: (set #x=0#)

#-2x + 7y = 14 \to 7y=14 \to y=2#

So, the #y# intercept is #(0,2)#

#x# intercept: (set #x=0#)

#-2x + 7y = 14 \to -2x=14 \to x=-7#

So, the #x# intercept is #(-7,0)#

To find the slope, it is convenient to write the equation in the form

#y = mx+q#

once this is done, the slope will be #m#. To reach or goal, let's add #2x# to both sides to get

#-2x + 7y = 14 \to 7y=2x+14#

and finally divide both sides by #7# to get

#y = 2/7 x + 2#

So, the slope is #2/7#