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Chapter 3: Q.471 (page 358)

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鈥搃ntercept form.

Short Answer

Expert verified

The equation of parallel line to the2x+5y=-10passing through the point(10,4)isy=-25x+8.

Step by step solution

01

Given information

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

02

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.

03

Explanation

We have,

2x+5y=-10

Rewriting it in to the slope - intercept form,

y=-25x+4

Comparing it with y = mx + b we get,

slope of the line is, m=-25.

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

Using slope point formula,

y-y1=m(x-x1)

Substituting the slope and given point,

y-4=-25(x-10)

Simplifying it,

y=-25x+8

04

Conclusion

Hence, equation of the parallel line to 2x+5y=-10passing through the point(10,4)isy=-25x+8.

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