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

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Answer 1 · 2018-06-20T15:25:57

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 $y=2.$

Answer 2 · 2018-06-20T15:26:35

$y$ 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 $x=0$ )

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

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 $2/7$