Question

Writing Equations of Lines Given the Graph
Write the slope-intercept form of the equation of each line.
questions are on the image below :)

Answer 1

Answer:

1. $y = 3x$

2. $y = -\frac{2}{3}x + 1$

3. $y = -\frac{2}{3}x - 4$

4. $y = 4$

5. $y = x + 5$

6. $y= \frac{5}{2}x$

7. $y = -7x -16$

8. $y = x + 4$

Step-by-step explanation:

The steps to solving these questions involve

1. Calculate slope using: $m = \frac{y_2 - y_1}{x_2 - x_1}$

2. Calculate the line equation using point slope formula: $y - y_1 = m(x - x_1)$

We'll apply the steps above in solving 1 through 8

Solving (1):

When x = 0; y = 0

When x = 1; y = 3

i.e.

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (1,3)$

Calculate slope:

$m=\frac{3 - 0}{1 - 0}$

$m=\frac{3 }{1 }$

$m = 3$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (0,0)$ and $m = 3$

$y - 0 = 3(x - 0)$

$y = 3x$

Solving (2):

When x = 0; y = 1

When x = 3; y = -1

i.e.

$(x_1,y_1) = (0,1)$

$(x_2,y_2) = (3,-1)$

Calculate slope:

$m=\frac{-1 - 1}{3 - 0}$

$m= -\frac{2}{3}$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (0,1)$ and $m= -\frac{2}{3}$

$y - 1 = -\frac{2}{3}(x - 0)$

$y - 1 = -\frac{2}{3}(x)$

$y - 1 = -\frac{2}{3}x$

$y = -\frac{2}{3}x + 1$

Solving (3):

When x = 0; y = -4

When x = -3; y = -2

i.e.

$(x_1,y_1) = (0,-4)$

$(x_2,y_2) = (-3,-2)$

Calculate slope:

$m=\frac{-2 - (-4)}{-3 - 0}$

$m=\frac{-2 +4}{-3 - 0}$

$m=\frac{2}{-3}$

$m=-\frac{2}{3}$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (0,-4)$ and $m= -\frac{2}{3}$

$y - (-4) = -\frac{2}{3}(x - 0)$

$y +4 = -\frac{2}{3}(x)$

$y +4 = -\frac{2}{3}x$

$y = -\frac{2}{3}x - 4$

Solving (4):

When x = 0; y = 4

When x = 4; y = 4

i.e.

$(x_1,y_1) = (0,4)$

$(x_2,y_2) = (4,4)$

Calculate slope:

$m=\frac{4 - 4}{4 - 0}$

$m=\frac{0}{4}$

$m = 0$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (0,4)$ and $m = 0$

$y - 4 = 0(x - 0)$

$y - 4 = 0$

$y = 4$

Solving (5):

When x = -4; y = 1

When x = -1; y = 4

i.e.

$(x_1,y_1) = (-4,1)$

$(x_2,y_2) = (-1,4)$

Calculate slope:

$m=\frac{4 - 1}{-1 - (-4)}$

$m=\frac{4 - 1}{-1 +4)}$

$m=\frac{3}{3)}$

$m = 1$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (-4,1)$ and $m = 1$

$y - 1 = 1(x - (-4))$

$y - 1 = 1(x +4)$

$y - 1 = x +4$

$y = x +4 + 1$

$y = x + 5$

Solving (6):

When x = 0; y = 0

When x = 2; y = 5

i.e.

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (2,5)$

Calculate slope:

$m=\frac{5 - 0}{2 - 0}$

$m=\frac{5 }{2 }$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (0,0)$ and $m=\frac{5 }{2 }$

$y - 0 = \frac{5}{2}(x - 0)$

$y - 0 = \frac{5}{2}(x)$

$y= \frac{5}{2}x$

Solving (7):

When x = -2; y = -2

When x = 2; y = 5

i.e.

$(x_1,y_1) = (-2,-2)$

$(x_2,y_2) = (-3,-5)$

Calculate slope:

$m=\frac{5 - (-2)}{-3 - (-2)}$

$m=\frac{5 +2}{-3 +2}$

$m=\frac{7}{-1}$

$m =-7$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (-2,-2)$ and $m =-7$

$y - (-2) = -7(x - (-2))$

$y +2 = -7(x +2)$

$y +2 = -7x -14$

$y = -7x -14 - 2$

$y = -7x -16$

Solving (8):

When x = -3; y = 1

When x = 0; y = 4

i.e.

$(x_1,y_1) = (-3,1)$

$(x_2,y_2) = (0,4)$

Calculate slope:

$m = \frac{4 - 1}{0 - (-3)}$

$m = \frac{4 - 1}{0 +3}$

$m = \frac{3}{3}$

$m = 1$

Next, we calculate the equation

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (-3,1)$ and $m = 1$

$y - 1 = 1(x - (-3))$

$y - 1 = 1(x +3)$

$y - 1 = x +3$

$y = x + 3 + 1$

$y = x + 4$