Given the line y=−2x+7 and the point (−1,10) , which of the following equations represents a line parallel to the given line and passing through the specified point?(1 point)

Question

Responses

y=−2x+12
y is equal to negative 2 x plus 12

y=−2x+8
y is equal to negative 2 x plus 8

y=2x+12
y is equal to 2 x plus 12

y=−12x+112

Answer 1

To find a line that is parallel to the given line \( y = -2x + 7 \) and passes through the point \((-1, 10)\), we need to remember that parallel lines have the same slope.

The slope of the given line \( y = -2x + 7 \) is \( -2 \).

A parallel line will also have a slope of \( -2 \) and can be expressed in the slope-intercept form \( y = mx + b \), where \( m = -2 \).

Now we can find the \( y \)-intercept \( b \) using the point \((-1, 10)\):

1. Substitute \( x = -1 \) and \( y = 10 \) into the equation \( y = mx + b \):

   \[ 10 = -2(-1) + b \]

   \[ 10 = 2 + b \]

   \[ b = 10 - 2 = 8 \]

Therefore, the equation of the line that is parallel to the given line and passes through the point \((-1, 10)\) is:

\[ y = -2x + 8 \]

So, the correct response is:

y = -2x + 8