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=0y=0 or -2x=142x=14 so is x=-7.x=7.

For the slope and y intercept we write 7y=2x+147y=2x+14 or y=2/7 x + 2y=27x+2 and read off the slope of 2/727 and y intercept at y=2.y=2.

Jun 20, 2018

yy intercept: (0,2)(0,2)

xx intercept: (-7,0)(7,0)

Slope: 2/727

Explanation:

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

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

-2x + 7y = 14 \to 7y=14 \to y=22x+7y=147y=14y=2

So, the yy intercept is (0,2)(0,2)

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

-2x + 7y = 14 \to -2x=14 \to x=-72x+7y=142x=14x=7

So, the xx intercept is (-7,0)(7,0)

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

y = mx+qy=mx+q

once this is done, the slope will be mm. To reach or goal, let's add 2x2x to both sides to get

-2x + 7y = 14 \to 7y=2x+142x+7y=147y=2x+14

and finally divide both sides by 77 to get

y = 2/7 x + 2y=27x+2

So, the slope is 2/727