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

Question

Responses

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

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

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

y=4/7x+5

Answer 1

To find a line perpendicular to the line \( y = -\frac{7}{4}x \), we first need to determine the slope of the given line. The slope of the line is \(-\frac{7}{4}\).

For two lines to be perpendicular, the product of their slopes must equal \(-1\). Thus, the slope \( m \) of the line we’re looking for can be found using:

\[ m \cdot \left(-\frac{7}{4}\right) = -1 \]

Solving for \( m \):

\[ m = \frac{4}{7} \]

Now, we have the slope of the perpendicular line, which is \( \frac{4}{7} \).

Next, we’ll use the point-slope form of the equation of a line to find the equation of the line with this slope that passes through the point \( (-7, 5) \):

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

Substituting in \( m = \frac{4}{7} \), \( x_1 = -7 \), and \( y_1 = 5 \):

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

Now, we can simplify this equation:

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

So the perpendicular line that goes through the point \((-7, 5)\) is

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

The correct response is:

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

Answer 2

Choose the equation of the line that is parallel to the x-axis.(1 point)
Responses

x=7
x equals 7

y=7x
y equals 7 x

y=7
y equals 7

x=7y

Answer 3

The equation of a line that is parallel to the x-axis has the same y-coordinate for all points on the line. This means that the equation will take the form \( y = k \), where \( k \) is a constant (the specific y-value).

Among the given options, the correct equation of the line that is parallel to the x-axis is:

y = 7

This means that for any value of \( x \), \( y \) will always equal 7.