Transform each linear equation to slope-intercept form.

Question

Match to each equation with the same equation in slope-intercept form.

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2x−5y+15=0

15y−2=x

4y−2x=−12

8x=2y−2

Answer 1

To transform each linear equation into slope-intercept form (y = mx + b), we'll rearrange the equations accordingly. Here are the transformations:

1. For the equation: \(2x - 5y + 15 = 0\):

   Rearranging gives: \[ -5y = -2x - 15 \] Dividing by -5: \[ y = \frac{2}{5}x + 3 \]

2. For the equation: \(15y - 2 = x\):

   Rearranging gives: \[ 15y = x + 2 \] Dividing by 15: \[ y = \frac{1}{15}x + \frac{2}{15} \]

3. For the equation: \(4y - 2x = -12\):

   Rearranging gives: \[ 4y = 2x - 12 \] Dividing by 4: \[ y = \frac{1}{2}x - 3 \]

4. For the equation: \(8x = 2y - 2\):

   Rearranging gives: \[ 2y = 8x + 2 \] Dividing by 2: \[ y = 4x + 1 \]

Now, summarizing the equations in slope-intercept form:

1. \( y = \frac{2}{5}x + 3 \)
2. \( y = \frac{1}{15}x + \frac{2}{15} \)
3. \( y = \frac{1}{2}x - 3 \)
4. \( y = 4x + 1 \)

Now, you can match these to the original equations you've been given.