WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points. $$ \begin{array}{lll} ext { 14. }(-1,-1),(1,5) & ext { 15. }(2,4),(3,6) & ext { 16. }(-2,3),(2,7) \ ext { 17. }(4,1),(8,2) & ext { 18. }(-9,5),(-3,3) & ext { 19. }(1,2),(-2,-1)\end{array} $$

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WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points. $$ \begin{array}{lll}	ext { 14. }(-1,-1),(1,5) & 	ext { 15. }(2,4),(3,6) & 	ext { 16. }(-2,3),(2,7) \ 	ext { 17. }(4,1),(8,2) & 	ext { 18. }(-9,5),(-3,3) & 	ext { 19. }(1,2),(-2,-1)\end{array} $$

UpStudy AI · Accepted Answer

To write the equation of a line in slope-intercept form $$y = mx + b$$, we need to determine the slope $$m$$ and the y-intercept $$b$$. The slope can be calculated using the formula:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Once we have the slope, we can use one of the points to solve for $$b$$ by substituting $$m$$, $$x$$, and $$y$$ into the equation $$y = mx + b$$.

Let's solve each pair of points step by step.

### 14. Points: $$(-1,-1)$$ and $$(1,5)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{5 - (-1)}{1 - (-1)} = \frac{5 + 1}{1 + 1} = \frac{6}{2} = 3
   $$

2. Use point $$(-1, -1)$$ to find $$b$$:
   $$
   -1 = 3(-1) + b \implies -1 = -3 + b \implies b = 2
   $$

3. The equation is:
   $$
   y = 3x + 2
   $$

### 15. Points: $$(2,4)$$ and $$(3,6)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{6 - 4}{3 - 2} = \frac{2}{1} = 2
   $$

2. Use point $$(2, 4)$$ to find $$b$$:
   $$
   4 = 2(2) + b \implies 4 = 4 + b \implies b = 0
   $$

3. The equation is:
   $$
   y = 2x + 0 \quad \text{or simply} \quad y = 2x
   $$

### 16. Points: $$(-2,3)$$ and $$(2,7)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{7 - 3}{2 - (-2)} = \frac{4}{4} = 1
   $$

2. Use point $$(-2, 3)$$ to find $$b$$:
   $$
   3 = 1(-2) + b \implies 3 = -2 + b \implies b = 5
   $$

3. The equation is:
   $$
   y = 1x + 5 \quad \text{or simply} \quad y = x + 5
   $$

### 17. Points: $$(4,1)$$ and $$(8,2)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{2 - 1}{8 - 4} = \frac{1}{4}
   $$

2. Use point $$(4, 1)$$ to find $$b$$:
   $$
   1 = \frac{1}{4}(4) + b \implies 1 = 1 + b \implies b = 0
   $$

3. The equation is:
   $$
   y = \frac{1}{4}x + 0 \quad \text{or simply} \quad y = \frac{1}{4}x
   $$

### 18. Points: $$(-9,5)$$ and $$(-3,3)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{3 - 5}{-3 - (-9)} = \frac{-2}{6} = -\frac{1}{3}
   $$

2. Use point $$(-9, 5)$$ to find $$b$$:
   $$
   5 = -\frac{1}{3}(-9) + b \implies 5 = 3 + b \implies b = 2
   $$

3. The equation is:
   $$
   y = -\frac{1}{3}x + 2
   $$

### 19. Points: $$(1,2)$$ and $$(-2,-1)$$

1. Calculate the slope $$m$$:
   $$
   m = \frac{-1 - 2}{-2 - 1} = \frac{-3}{-3} = 1
   $$

2. Use point $$(1, 2)$$ to find $$b$$:
   $$
   2 = 1(1) + b \implies 2 = 1 + b \implies b = 1
   $$

3. The equation is:
   $$
   y = 1x + 1 \quad \text{or simply} \quad y = x + 1
   $$

### Summary of Equations
1. $$y = 3x + 2$$
2. $$y = 2x$$
3. $$y = x + 5$$
4. $$y = \frac{1}{4}x$$
5. $$y = -\frac{1}{3}x + 2$$
6. $$y = x + 1$$
Here are the equations of the lines in slope-intercept form for each pair of points: 1. $$ y = 3x + 2 $$ 2. $$ y = 2x $$ 3. $$ y = x + 5 $$ 4. $$ y = \frac{1}{4}x $$ 5. $$ y = -\frac{1}{3}x + 2 $$ 6. $$ y = x + 1 $$

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