Question

Find the equation of the line with slope = -1 and passing through (10,-2).

Answer 1

Answer and Step-by-step explanation:

To find the equation of a line with a given slope and passing through a given point, we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents the given point and m represents the slope.

In this case, the given slope is -1, and the point the line passes through is (10, -2). Plugging these values into the point-slope form, we have:

y - (-2) = -1(x - 10)

Simplifying the equation further:

y + 2 = -x + 10

To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y:

y = -x + 10 - 2

Simplifying further:

y = -x + 8

Therefore, the equation of the line with a slope of -1 and passing through the point (10, -2) is y = -x + 8.

Answer 2

Slope

With the givens (slope = -1 and point (10,-2) we will find the equation.

I'll use the slope intercept equation, y = mx + c,

where m is the slope and c is the y-intercept

y = -1x + c

y = -x + c

now, plug in the point

-2 = -10 + c

-2 + 10 = c

8 = c

The equation is calculated as y = -x + 8.