Question

this is a 2-page document
directions: graph each equation. show all work for standard form to slope-intercept form conversions

1. $y = -\frac{7}{4}x + 1$
2. $y = \frac{1}{3}x + 4$
3. $y = -x - 3$
4. $y = 6x + 2$
5. $y = -7 + 4x$
6. $y = -1 - \frac{2}{5}x$
7. $3x + y = -5$
8. $x - y = 0$

Explanation:

For Equations 1-6 (already slope-intercept form $y=mx+b$, where $m$=slope, $b$=y-intercept):

Step1: Identify slope and intercept

For each equation, extract $m$ and $b$:

1. $y=-\frac{7}{4}x+1$: $m=-\frac{7}{4}$, $b=1$
2. $y=\frac{1}{3}x+4$: $m=\frac{1}{3}$, $b=4$
3. $y=-x-3$: $m=-1$, $b=-3$
4. $y=6x+2$: $m=6$, $b=2$
5. $y=4x-7$: $m=4$, $b=-7$ (rewrote $-7+4x$ to standard slope-intercept)
6. $y=-\frac{2}{5}x-1$: $m=-\frac{2}{5}$, $b=-1$ (rewrote $-1-\frac{2}{5}x$ to standard slope-intercept)

Step2: Plot y-intercept

Mark the point $(0, b)$ on the y-axis for each equation.

Step3: Use slope to find second point

Slope $m=\frac{\text{rise}}{\text{run}}$:

1. For $m=-\frac{7}{4}$: from $(0,1)$, move down 7, right 4 to $(4,-6)$
2. For $m=\frac{1}{3}$: from $(0,4)$, move up 1, right 3 to $(3,5)$
3. For $m=-1$: from $(0,-3)$, move down 1, right 1 to $(1,-4)$
4. For $m=6$: from $(0,2)$, move up 6, right 1 to $(1,8)$
5. For $m=4$: from $(0,-7)$, move up 4, right 1 to $(1,-3)$
6. For $m=-\frac{2}{5}$: from $(0,-1)$, move down 2, right 5 to $(5,-3)$

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For Equations 7-8 (convert to slope-intercept form first):

Step1: Isolate $y$ for $3x+y=-5$

Subtract $3x$ from both sides:
$y = -3x -5$
Here, $m=-3$, $b=-5$

Step2: Isolate $y$ for $x-y=0$

Subtract $x$ and multiply by $-1$:
$y = x$
Here, $m=1$, $b=0$

Step3: Plot intercepts and slope points

1. For $y=-3x-5$: plot $(0,-5)$, then move down 3, right 1 to $(1,-8)$
2. For $y=x$: plot $(0,0)$, then move up 1, right 1 to $(1,1)$

Step4: Draw lines

Connect the two points for each equation to form the straight line.

Answer:

1. Line for $y=-\frac{7}{4}x+1$: passes through $(0,1)$ and $(4,-6)$
2. Line for $y=\frac{1}{3}x+4$: passes through $(0,4)$ and $(3,5)$
3. Line for $y=-x-3$: passes through $(0,-3)$ and $(1,-4)$
4. Line for $y=6x+2$: passes through $(0,2)$ and $(1,8)$
5. Line for $y=4x-7$: passes through $(0,-7)$ and $(1,-3)$
6. Line for $y=-\frac{2}{5}x-1$: passes through $(0,-1)$ and $(5,-3)$
7. Line for $y=-3x-5$: passes through $(0,-5)$ and $(1,-8)$
8. Line for $y=x$: passes through $(0,0)$ and $(1,1)$

To graph, mark these points on the respective grids and draw a straight line through each pair.