2 Find the equation of a line paralle)
to and passiog through

Ask by Knight Salazar. in Nigeria

Jan 21,2025

Question

2 Find the equation of a line paralle) to $$ y=1 / 3 x-4 $$ and passiog through $$ (5,0) $$

UpStudy AI · Accepted Answer

To find the equation of a line that is **parallel** to $$ y = \frac{1}{3}x - 4 $$ and **passes through the point** $$ (5, 0) $$, follow these steps:

1. **Identify the Slope of the Given Line:**
   - The slope-intercept form of a line is $$ y = mx + b $$, where $$ m $$ is the slope.
   - For $$ y = \frac{1}{3}x - 4 $$, the slope $$ m = \frac{1}{3} $$.

2. **Use the Same Slope for the Parallel Line:**
   - Since parallel lines have the same slope, the new line will also have a slope of $$ \frac{1}{3} $$.

3. **Use the Point-Slope Form to Find the Equation:**
   - The point-slope form is $$ y - y_1 = m(x - x_1) $$, where $$ (x_1, y_1) $$ is a point on the line.
   - Plugging in the slope $$ m = \frac{1}{3} $$ and the point $$ (5, 0) $$:
     $$
     y - 0 = \frac{1}{3}(x - 5)
     $$
     $$
     y = \frac{1}{3}x - \frac{5}{3}
     $$

4. **Final Equation:**
   - The equation of the desired line in slope-intercept form is:
     $$
     y = \frac{1}{3}x - \frac{5}{3}
     $$

**Therefore, the equation of the parallel line passing through $$ (5, 0) $$ is:**

$$
y = \frac{1}{3}x - \frac{5}{3}
$$
The equation of the line parallel to $$ y = \frac{1}{3}x - 4 $$ and passing through $$ (5, 0) $$ is $$ y = \frac{1}{3}x - \frac{5}{3} $$.

2 Find the equation of a line paralle)
to and passiog through

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2 Find the equation of a line paralle) to and passiog through