Question

Math pls help n show work

Answer 1

The equation of the line passing through (0, 2) and (3, 0) is (2x + 3y = 6), as derived from the slope-intercept form. (option A)

To determine the equation of the line passing through the points (0, 2) and (3, 0), we can use the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

First, calculate the slope (m):

`\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} \]\[ m = \frac{{0 - 2}}{{3 - 0}} = \frac{{-2}}{{3}} \]`

Now, plug one of the points (let's use (0, 2)) and the calculated slope into the slope-intercept form to find the y-intercept (b):

`\[ 2 = \frac{{-2}}{{3}} \cdot 0 + b \]\[ b = 2 \]`

The equation of the line is then:

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

Now, rearrange this equation to one of the given options:

`\[ 2x + 3y = 6 \]`

So, the correct answer is:

`\[ \text{{A. }} 2x + 3y = 6 \]`