Find the equation of the line that contains the point P(2, 5) and is parallel to the graph of 5x + y = −4.

Answer 1

Hi Danielle,

If we want to find the equation of the line that contains the point P(2, 5) and is parallel to the graph of 5x + y = -4, we would first want to ensure we understand what the slope of the graph is.

To find the slope, we can rewrite the linear equation provided 5x + y = --4 into slope-intercept form,

y = mx + b, with m representing the slope, and b representing the y-intercept.

5x + y = -4, If we subtract 5x on both sides to solve for y, we get:

y = -5x - 4

The slope m therefore equals -5. The line that will be parallel to this will also have a slope of -5 (so that the line goes in the same direction/has the same steepness).

We know that this line needs to pass through P(2, 5) as well. We can use the point-slope form of the linear equation to help with this. The point-slope form is y-y₁ = m(x-x₁) with (x₁, y₁) being the x and y coordinates of the point P provided. If we substitute the slope m = -5 and have x₁ = 2 and y₁ = 5. We get:

Answer in point-slope form: y - 5 = -5(x - 2)

There is your equation of the line! If you need to rewrite the equation of the line into slope-intercept form, you may certainly do so by algebraically rearranging it:

y - 5 = -5(x - 2) ---> Distribute.

y - 5 = -5x + 10 ----> Add 5 to both sides.

Answer in slope-intercept form: y = -5x + 15

If you have any questions, let me know. There is a little more to explore with this if you are interested!

Thanks!