Given 2x - y = 8, identify the slope and y-intercept.

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Understand the Problem

The question is asking to identify the slope (m) and y-intercept (b) of the linear equation given in standard form. We need to manipulate the equation into slope-intercept form (y = mx + b) to extract these values.

Answer

m = 2, b = -8
Answer for screen readers

m = 2

b = -8

Steps to Solve

  1. Rearranging the equation

Start with the given equation in standard form: $$ 2x - y = 8 $$

Next, isolate $y$ on one side of the equation. This can be done by subtracting $2x$ from both sides:

$$ -y = -2x + 8 $$

  1. Multiplying to eliminate negative sign

To get $y$ by itself, multiply both sides by $-1$:

$$ y = 2x - 8 $$

  1. Identifying slope and y-intercept

Now that the equation is in slope-intercept form ($y = mx + b$), we can identify the slope ($m$) and the y-intercept ($b$):

  • The slope $m = 2$ (the coefficient of $x$)
  • The y-intercept $b = -8$

m = 2

b = -8

More Information

The slope ($m$) indicates that for each increase of 1 in $x$, $y$ increases by 2. The y-intercept ($b$) tells us that the line crosses the y-axis at -8.

Tips

  • Not changing the signs when isolating $y$. Remember to multiply through by -1.
  • Confusing the slope and y-intercept in the final equation. Always check coefficients and constant terms.
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