Question

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

Short answer

The equation of parallel line to the$2x+5y=-10$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 $2x+5y=-10$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,

$2x+5y=-10$

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