Question

Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?

y – 2 = 3(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y – 3 = 2(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y + y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis. = 3(x – 2)
y + y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis. = 2(x – 3)

Answer 1

Answer:

Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?

y – 2 = 3(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)

y – 3 = 2(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)

y + y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis. = 3(x – 2)

y + y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis. = 2(x – 3)

Answer 2

The equation represents a Line is $y + 1/2 = 3(x-2)$

Given:

A line that passes through (2, -1/2) and has a slope of 3

To find:

The equation represents a line

Solution:

The equation of a line for a line with slope m passing through the points $(x_{1} , y_{1} )$  is $(y-y_{1} ) = m(x-x_{1} )$.

So, m = 3, x₁ = 2, y₁ = -1/2

Substitute the above values in the equation of a line

⇒ $y - (-1/2) = 3(x - 2)$

⇒ $y + 1/2 = 3(x - 2)$

⇒ $2y + 1 = 6(x - 2)$

⇒ $2y + 1 = 6x - 12$

⇒ $6x - 2y = 13$

⇒ $y + 1/2 = 3(x-2)$

Therefore, the equation represents a Line is $y + 1/2 = 3(x-2)$

#SPJ2