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

Question

Hazel Anglin · Accepted Answer

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.#

Ethan Adkins · Answer

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

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

Slope: #2/7# To find the intercepts, set one of the coordinates to zero and solve for the other: #y# intercept: (set #x=0#) #-2x + 7y = 14 o 7y=14 o y=2# So, the #y# intercept is #(0,2)# #x# intercept: (set #x=0#) #-2x + 7y = 14 o -2x=14 o 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 o 7y=2x+14# and finally divide both sides by #7# to get #y = 2/7 x + 2# So, the slope is #2/7#

Avery Alexander · Answer

undefined To find the x-intercept:
1. Set y = 0 in the equation: -2x + 7(0) = 14.
2. Solve for x: -2x = 14.
3. Divide both sides by -2: x = -7.

To find the y-intercept:
1. Set x = 0 in the equation: -2(0) + 7y = 14.
2. Solve for y: 7y = 14.
3. Divide both sides by 7: y = 2.

To find the slope:
1. Rewrite the equation in slope-intercept form: y = mx + b.
2. Solve for y: 7y = 2x + 14.
3. Divide both sides by 7: y = (2/7)x + 2.
4. The slope, m, is the coefficient of x: m = 2/7.

To graph the line:
1. Plot the x-intercept (-7, 0) and the y-intercept (0, 2).
2. Use the slope to find additional points if needed.
3. Draw a straight line through the points to represent the graph of the equation.