To find the equation of the line that passes through the point [tex]\((0,0)\)[/tex] with a slope of [tex]\(-\frac{3}{4}\)[/tex], we can follow these steps:
1. Identify the standard form of the line equation:
The equation of a line in slope-intercept form is given by:
[tex]\[
y = mx + b
\][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
2. Substitute the given slope:
We are given the slope [tex]\( m = -\frac{3}{4} \)[/tex].
So the equation becomes:
[tex]\[
y = -\frac{3}{4}x + b
\][/tex]
3. Determine the y-intercept [tex]\(b\)[/tex]:
The line passes through the point [tex]\((0,0)\)[/tex]. When [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex], we can substitute these values into the equation to solve for [tex]\(b\)[/tex]:
[tex]\[
0 = -\frac{3}{4} \cdot 0 + b \implies b = 0
\][/tex]
4. Write the final equation:
With [tex]\( m = -\frac{3}{4} \)[/tex] and [tex]\( b = 0 \)[/tex], the equation of the line is:
[tex]\[
y = -\frac{3}{4}x + 0
\][/tex]
Simplifying this, we get:
[tex]\[
y = -0.75x + 0
\][/tex]
Therefore, the equation of the line through [tex]\((0,0)\)[/tex] with a slope of [tex]\(-\frac{3}{4}\)[/tex] is:
[tex]\[
y = -0.75x + 0
\][/tex]
