Question

Which line is perpendicular to the line y=−7/4x and goes through the point (−7,5) ?(1 point)
Responses

y=4/7x+5
y equals Start Fraction 4 over 7 End Fraction x plus 5

y=−7/4x+5
y equals negative Start Fraction 7 over 4 End Fraction x plus 5

y=4/7x+9
y equals Start Fraction 4 over 7 End Fraction x plus 9

y=−4/7x+1

Answer 1

To find a line that is perpendicular to the line given by \( y = -\frac{7}{4}x \) and passes through the point \((-7, 5)\), we need to determine the slope of the perpendicular line.

1. The slope of the given line \( y = -\frac{7}{4}x \) is \( -\frac{7}{4} \).
2. The slope of a line perpendicular to it is the negative reciprocal of \( -\frac{7}{4} \), which is \( \frac{4}{7} \).

Now, we can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point through which the line passes, and \( m \) is the slope.

Plugging in the point \((-7, 5)\) and the slope \( \frac{4}{7} \):

\[
y - 5 = \frac{4}{7}(x + 7)
\]

Now, we can simplify this equation:

\[
y - 5 = \frac{4}{7}x + 4
\]
\[
y = \frac{4}{7}x + 4 + 5
\]
\[
y = \frac{4}{7}x + 9
\]

So the equation of the line that is perpendicular to \( y = -\frac{7}{4}x \) and goes through the point \((-7, 5)\) is:

\[
\boxed{y = \frac{4}{7}x + 9}
\]

Therefore, the correct response is:

**y = \( \frac{4}{7}x + 9 \)**.