Question

Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 12, comma, 15, right bracket(−12,15) with slope minus, 1−1

Answer 1

The point-slope form of a linear equation is given by:

y − y₁ = m(x − x₁)

where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.

Using the given point (-12, 15) and slope -1, we can plug these values into the point-slope form and get the equation:

y − 15 = -1(x − (-12))

Simplifying the equation:

y − 15 = -1(x + 12)

Expanding the brackets:

y − 15 = -x - 12

Rearranging the equation:

y = -x - 12 + 15

Simplifying further:

y = -x + 3

Therefore, the equation of the line that passes through the point (-12, 15) with a slope of -1 is y = -x + 3.