Question

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directions: identify the slope and y - intercept of each equation, then graph the line.

1. $y = x - 2$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = -\frac{7}{5}x + 3$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = 3x$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = -4x - 1$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = -\frac{1}{6}x + 2$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = \frac{5}{2}x + 8$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = \frac{1}{4}x - 7$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

1. $y = -x + 4$

$m = \underline{\quad}$
$b = \underline{\quad}$
graph

Explanation:

All equations use slope-intercept form $y=mx+b$, where $m$ = slope, $b$ = y-intercept.

Step1: Match to $y=mx+b$

For each equation, identify $m$ (coefficient of $x$) and $b$ (constant term).

Equation 2: $y=-\frac{7}{5}x+3$

$m=-\frac{7}{5}$, $b=3$

Equation 3: $y=3x$

Rewrite as $y=3x+0$, so $m=3$, $b=0$

Equation 4: $y=-4x-1$

$m=-4$, $b=-1$

Equation 5: $y=-\frac{1}{6}x+2$

$m=-\frac{1}{6}$, $b=2$

Equation 6: $y=\frac{5}{2}x+8$

$m=\frac{5}{2}$, $b=8$

Equation 7: $y=\frac{1}{4}x-7$

$m=\frac{1}{4}$, $b=-7$

Equation 8: $y=-x+4$

Rewrite as $y=-1x+4$, so $m=-1$, $b=4$

Step2: Confirm given Equation 1

$y=x-2$ is $y=1x-2$, so $m=1$, $b=-2$ (matches provided answers)

Answer:

1. $m=1$, $b=-2$
2. $m=-\frac{7}{5}$, $b=3$
3. $m=3$, $b=0$
4. $m=-4$, $b=-1$
5. $m=-\frac{1}{6}$, $b=2$
6. $m=\frac{5}{2}$, $b=8$
7. $m=\frac{1}{4}$, $b=-7$
8. $m=-1$, $b=4$

Graphing Guidance (for each line):

• Plot the y-intercept $(0, b)$ first.
• Use slope $m=\frac{\text{rise}}{\text{run}}$ to plot a second point:
• For positive $m$: rise up, run right; for negative $m$: rise down, run right (or rise up, run left)
• Draw a straight line through the two points.