Question

What is the equation of the like that passes through the point (-4,2) and has a slope of -1

Answer 1

y= mx+b (m is the slope)

The equation of a line can be determined using the point-slope form, which is given by the equation y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

In this case, the given point is (-4, 2) and the slope is -1. Plugging these values into the point-slope form, we get:

y - 2 = -1(x - (-4))

Simplifying further, we have:

y - 2 = -1(x + 4)

Distributing the -1 on the right side, we get:

y - 2 = -x - 4

To isolate y, we can add x to both sides:

y = -x - 4 + 2

Simplifying, we have:

y = -x - 2

Therefore, the equation of the line that passes through the point (-4, 2) and has a slope of -1 is y = -x - 2.

Answer 2

y = - x - 2

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given slope m = - 1 , then

y = - x + c ← is the partial equation

to find c, substitute the point (- 4, 2 ) for x and y into the partial equation

2 = - (- 4) + c = 4 + c ( subtract 4 from both sides )

- 2 = c

y = - x - 2 ← equation of line