Question

graph the line using the given slope and the y-intercept.

1. slope = $\frac{7}{6}$; y-intercept = -1
2. slope = -4; y-intercept = 7
3. slope = $\frac{5}{7}$; y-intercept = -6
4. slope = 8; y-intercept = -4
5. slope = $\frac{3}{4}$; y-intercept = 2
6. slope = -1; y-intercept = -3
7. slope = 5; y-intercept = 3
8. slope = -2; y-intercept = -2
9. slope = $\frac{3}{5}$; y-intercept = 4

Explanation:

Step1: Write line equation (slope-intercept)

For each problem, use $y = mx + b$, where $m$ = slope, $b$ = y-intercept:

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

Step2: Plot y-intercept first

Mark the point $(0, b)$ on each grid:

1. $(0, -1)$
2. $(0, 7)$
3. $(0, -6)$
4. $(0, -4)$
5. $(0, 2)$
6. $(0, -3)$
7. $(0, 3)$
8. $(0, -2)$
9. $(0, 4)$

Step3: Use slope for second point

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

1. Rise = -7, Run = 6 → from $(0,-1)$, move 6 right, 7 down to $(6, -8)$
2. Rise = -4, Run = 1 → from $(0,7)$, move 1 right, 4 down to $(1, 3)$
3. Rise = 5, Run = 7 → from $(0,-6)$, move 7 right, 5 up to $(7, -1)$
4. Rise = 8, Run = 1 → from $(0,-4)$, move 1 right, 8 up to $(1, 4)$
5. Rise = 3, Run = 4 → from $(0,2)$, move 4 right, 3 up to $(4, 5)$
6. Rise = -1, Run = 1 → from $(0,-3)$, move 1 right, 1 down to $(1, -4)$
7. Rise = 5, Run = 1 → from $(0,3)$, move 1 right, 5 up to $(1, 8)$
8. Rise = -2, Run = 1 → from $(0,-2)$, move 1 right, 2 down to $(1, -4)$
9. Rise = -3, Run = 5 → from $(0,4)$, move 5 right, 3 down to $(5, 1)$

Step4: Draw line through points

Connect the two plotted points on each grid with a straight line, extending across the grid.

Answer:

1. Line passes through $(0, -1)$ and $(6, -8)$
2. Line passes through $(0, 7)$ and $(1, 3)$
3. Line passes through $(0, -6)$ and $(7, -1)$
4. Line passes through $(0, -4)$ and $(1, 4)$
5. Line passes through $(0, 2)$ and $(4, 5)$
6. Line passes through $(0, -3)$ and $(1, -4)$
7. Line passes through $(0, 3)$ and $(1, 8)$
8. Line passes through $(0, -2)$ and $(1, -4)$
9. Line passes through $(0, 4)$ and $(5, 1)$

(When graphing, draw a straight line through each pair of points on the corresponding grid.)