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Which of the following is an equation of the line in the
xy-plane that passes through the point
(1,1) and is parallel to the line with equation
y=-3x-1 ?
Choose 1 answer:
(A)
y=(1)/(3)x+4
(B)
y=(1)/(3)x+1
(C)
y=-3x+4
(D)
y=-3x+1

Which of the following is an equation of the line in the $x y$ -plane that passes through the point $(1,1)$ and is parallel to the line with equation $y=-3 x-1$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{1}{3} x+4$ $\newline$ (B) $y=\frac{1}{3} x+1$ $\newline$ (C) $y=-3 x+4$ $\newline$ (D) $y=-3 x+1$

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Find equations of tangent lines using limits

Full solution

Q. Which of the following is an equation of the line in the

x y

-plane that passes through the point

(1,1)

and is parallel to the line with equation

y=-3 x-1

?

\newline

Choose

1

answer:

\newline

(A)

y=\frac{1}{3} x+4

\newline

(B)

y=\frac{1}{3} x+1

\newline

(C)

y=-3 x+4

\newline

(D)

y=-3 x+1

Identify slope of line: Parallel lines have the same slope. The slope of the given line $y=-3x-1$ is $-3$ .
Use point-slope form: Use the point-slope form of a line equation, $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through.
Plug in slope and point: Plug in the slope $-3$ and the point $(1,1)$ into the point-slope form: $y - 1 = -3(x - 1)$ .
Simplify the equation: Simplify the equation: $y - 1 = -3x + 3$ .
Isolate $y$ variable: Add $1$ to both sides to get $y$ by itself: $y = -3x + 3 + 1$ .
Combine like terms: Combine like terms: $y = -3x + 4$ .

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