Find the equation of a line that passes through (2, -3) and that is parallel to 5x + y= -2

Answer 1

When two lines are parallel, they will have the same slope.

5x + y = -2 → y = -5x - 2

We are given a point (2, -3). We need to find the second line that is parallel to the first.

Use the point-slope form.

y - y₀ = m(x - x₀)

y - (-3) = -5(x - 2)

y + 3 = -5x + 10

y = -5x + 7

5x + y = 7

The final answer is written in standard form.

Answer 2

Hello, Ashley,

Let's rewrite the equation in a more conventional form:

y = mx + b, where m is the slope and b is the y axis intercept. It is the value of y when x = 0.

y = -5x -2

In this form, the coefficient of x, -5, is the slope of the line. Slope is the "rise"/"run" of the line. It tells us the the line goes down 5 (-5) each time x goes up by 1. The rise is y moving -5 and the run is the x as it increase by 1, so the slope is -5. The line is moving down as it heads to the right. The -2 in the equation is the point on y that the line crosses it when x = 0.

The question wants the equation of a parallel line that intersects (2, -3). I've marked that point on the graph below. To be parallel, it must have the same slope, -5.

Rewrite the equation to reflect the same slope. We don't know b yet:

y = -5x + b

We do know the line goes through (2, -3). Since that is a solution to the equation, we can substitute the numbers to find b:

-3 = -5*(2) + b

b = 3 -10

b = 7

The equation we want is y = -5x + 7. (Green line)

The line intercepts the y axis at (0,7) and is parallel to the original (red) line.

I hope this helps,

Bob