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

For the slope and y intercept we write $7 y = 2 x + 14$ $7y=2x+14$ or $y = \frac{2}{7} x + 2$ $y=2/7 x + 2$ and read off the slope of $\frac{2}{7}$ $2/7$ and y intercept at $y = 2 .$ $y=2.$

Answer 2 · 2018-06-20T15:26:35

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

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

Slope: $\frac{2}{7}$ $2/7$

Explanation:

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

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

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

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

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

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

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

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

$y = m x + q$ $y = mx+q$

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

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

and finally divide both sides by $7$ $7$ to get

$y = \frac{2}{7} x + 2$ $y = 2/7 x + 2$

So, the slope is $\frac{2}{7}$ $2/7$

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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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