writing linear eqautions from standard form to slope-intercept form

Question

7x-2y=-6

Answer 1

To convert the linear equation from standard form to slope-intercept form, you'll want to solve for \( y \) in terms of \( x \). The standard form is given by:

\[ 7x - 2y = -6 \]

To put this into slope-intercept form, \( y = mx + b \), follow these steps:

1. Isolate the term with \( y \):

   \[ -2y = -7x - 6 \]

2. Divide every term by \(-2\) to solve for \( y \):

   \[ y = \frac{7}{2}x + 3 \]

Now, the equation is in slope-intercept form, where the slope \( m \) is \( \frac{7}{2} \) and the y-intercept \( b \) is \( 3 \).

So, the final slope-intercept form of the equation is:

\[ y = \frac{7}{2}x + 3 \]