Question

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

y=−4/7x+1
y equals negative Start Fraction 4 over 7 End Fraction x plus 1

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

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

y=−7/4x+5

Answer 1

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

The slope of the given line \( y = -\frac{7}{4}x \) is \(-\frac{7}{4}\). The slope of a line that is perpendicular to it can be found using the negative reciprocal of this slope.

The negative reciprocal of \(-\frac{7}{4}\) is:
\[
\frac{4}{7}
\]

Now, we use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope and \((x_1, y_1)\) is the point through which the line passes.

Here, \(m = \frac{4}{7}\), \(x_1 = -7\), and \(y_1 = 5\).

Plugging the values into the point-slope form gives:
\[
y - 5 = \frac{4}{7}(x + 7)
\]

Now simplifying:
\[
y - 5 = \frac{4}{7}x + \frac{4}{7} \cdot 7
\]
\[
y - 5 = \frac{4}{7}x + 4
\]
\[
y = \frac{4}{7}x + 4 + 5
\]
\[
y = \frac{4}{7}x + 9
\]

Thus, the equation of the line that is perpendicular to \( y = -\frac{7}{4}x \) and passes through the point \((-7, 5)\) is:
\[
y = \frac{4}{7}x + 9
\]

Therefore, the correct response is:
**y = 4/7x + 9**.