Question

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

2x + 5y = −10, point (10, 4)

Short answer

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

Step-by-step solution

Step 1. Given information

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

Step 2. Concepts 

Here first we can write the given equation in the form of y = mx + b and to find the equation of parallel line we can use the slope point formula.

Slope - point formula: $y-y_1=m(x-x_1)$

Where, m is the slope and$(x_1,y_1)$is the given point.

Step 3. Explanation

Rewriting 2x + 5y = -10 in to the slope intercept form,

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

Comparing it with y = mx + b we get,

slope of the given line is $-\frac{2}{5}$.

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

Now using slope point formula and given point we get,

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

Simplifying it,

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

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

Step 4. Conclusion

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