To find the equation of a line in slope-intercept form (which is [tex]\( y = mx + b \)[/tex]), given a point and a slope, we need to follow a systematic process. We are given the point [tex]\((-4, 0)\)[/tex] and the slope [tex]\( m = -\frac{3}{5} \)[/tex].
1. Start with the point-slope form of the line equation:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is the given point and [tex]\(m\)[/tex] is the slope.
2. Substitute the given point [tex]\((-4, 0)\)[/tex] and the slope [tex]\(m = -\frac{3}{5}\)[/tex] into the point-slope equation:
[tex]\[
y - 0 = -\frac{3}{5}(x - (-4))
\][/tex]
Simplify within the parenthesis:
[tex]\[
y = -\frac{3}{5}(x + 4)
\][/tex]
3. Distribute the slope [tex]\(-\frac{3}{5}\)[/tex] through the parentheses:
[tex]\[
y = -\frac{3}{5}x - \frac{3}{5} \cdot 4
\][/tex]
4. Calculate [tex]\(-\frac{3}{5} \cdot 4\)[/tex]:
[tex]\[
-\frac{3}{5} \cdot 4 = -\frac{12}{5}
\][/tex]
5. Therefore, the equation in slope-intercept form is:
[tex]\[
y = -\frac{3}{5}x - \frac{12}{5}
\][/tex]
Thus, the correct equation of the line in slope-intercept form is:
[tex]\[
y = -\frac{3}{5}x - \frac{12}{5}
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
y = -\frac{3}{5}x - \frac{12}{5}
\][/tex]
