Chapter 3: Q.471 (page 358)

Find an equation of a line parallel to the given line $2 x + 5 y = - 10$ and contains the given point $(10, 4)$ . Write the equation in slope–intercept form.

Short Answer

Expert verified

The equation of parallel line to the $2 x + 5 y = - 10$ passing through the point $(10, 4)$ is $y = - \frac{2}{5} x + 8$ .

Step by step solution

Given information

We have given equation of the line is $2 x + 5 y = - 10$ and point is $(10, 4)$ .

Concepts

First need to write original equation in the form of y = mx + b.

Then we will use slope - point formula to find the equation of parallel line to the original line passing through the given point.

Explanation

We have,

$2 x + 5 y = - 10$

Rewriting it in to the slope - intercept form,

$y = - \frac{2}{5} x + 4$

Comparing it with y = mx + b we get,

slope of the line is, $m = - \frac{2}{5}$ .

We know that two lines are parallel if their slopes are equal and they have different y-intercepts.

Using slope point formula,

$y - y_{1} = m (x - x_{1})$

Substituting the slope and given point,

$y - 4 = - \frac{2}{5} (x - 10)$

Simplifying it,

$y = - \frac{2}{5} x + 8$

Conclusion

Hence, equation of the parallel line to $2 x + 5 y = - 10$ passing through the point $(10, 4)$ is $y = - \frac{2}{5} x + 8$ .

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Find an equation of a line parallel to the given line $2 x + 5 y = - 10$ and contains the given point $(10, 4)$ . Write the equation in slope–intercept form.

Short Answer

Step by step solution

Given information

Concepts

Explanation

Conclusion

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Find an equation of a line parallel to the given line 2x+5y=-10and contains the given point(10,4). Write the equation in slope–intercept form.

Short Answer

Step by step solution

Given information

Concepts

Explanation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find an equation of a line parallel to the given line $2 x + 5 y = - 10$ and contains the given point $(10, 4)$ . Write the equation in slope–intercept form.