Question

A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?

A y-3=-2(x - 2)
By+3 = -2(x+2)
Cy=-2x+7
D 2x+y=7
E
y=--x+5

Answer 1

`\textsf{A.} \quad y-3=-2(x-2)`

Explanation:

`\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}`

Given values:

• m = -2
• (x₁, y₁) = (2, 3)

To find the equation of the line in point-slope form, substitute the given slope and point into the point-slope formula:

`\implies y-y_1=m(x-x_1)`

`\implies y-3=-2(x-2)`

Answer 2

• A) y - 3 = - 2(x - 2)

========================

Point-slope form is:

• y - y₁ = m(x - x₁), where (x₁, y₁) is the coordinates of the point, m is the slope

Substitute the values to get:

• x₁ = 2, y₁ = 3, m = - 2

• y - 3 = - 2(x - 2)

The matching choice is A