Certainly! Let's find the equation of the line that passes through the point [tex]\((0,0)\)[/tex] with a slope of [tex]\(-\frac{3}{4}\)[/tex].
### Step-by-Step Solution:
1. Identify the Point and the Slope:
- Point: [tex]\((x_1, y_1) = (0, 0)\)[/tex]
- Slope: [tex]\(m = -\frac{3}{4}\)[/tex]
2. Use the Point-Slope Formula:
The point-slope form of a line's equation is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Plugging in the given point and slope:
[tex]\[
y - 0 = -\frac{3}{4}(x - 0)
\][/tex]
3. Simplify the Equation:
Since [tex]\(y_1 = 0\)[/tex] and [tex]\(x_1 = 0\)[/tex], the equation simplifies to:
[tex]\[
y = -\frac{3}{4}x
\][/tex]
4. Write the Equation in Slope-Intercept Form:
The slope-intercept form of a line's equation is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept. From the simplified equation above:
[tex]\[
y = -\frac{3}{4}x + 0
\][/tex]
5. Final Equation:
The equation of the line in slope-intercept form is:
[tex]\[
y = -0.75x + 0.0
\][/tex]
Hence, the equation of the line passing through the point [tex]\((0, 0)\)[/tex] with a slope of [tex]\(-\frac{3}{4}\)[/tex] is:
[tex]\[
y = -0.75x + 0.0
\][/tex]
