Question

Consider the line 5x+2y=−4. What is the equation of the line parallel to the given line that passes through the point (−2, 6) in slope-intercept form? Enter your answer by filling in the boxes to complete the equation.

Answer 1

y = -5/2x +1

Explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

Parallel line

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

5(-2) +2(6) = c

-10 +12 = c

2 = c

Now we know the equation of the parallel line can be written as ...

5x +2y = 2

Slope-intercept form

Solving for y puts this in slope-intercept form:

2y = -5x +2 . . . . . . . . subtract 5x

y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

`\boxed{y=(-5)/(2)x+1}`

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