Question

Which line is perpendicular to the line y=−74x and goes through the point (−7,5) ?(1 point)
Responses

y=47x+9
y equals Start Fraction 4 over 7 End Fraction x plus 9

y=−74x+5
y equals negative Start Fraction 7 over 4 End Fraction x plus 5

y=−47x+1
y equals negative Start Fraction 4 over 7 End Fraction x plus 1

y=47x+5

Answer 1

To find a line that is perpendicular to the line given by the equation \( y = -74x \) and goes through the point \( (-7, 5) \), we first need to determine the slope of the given line.

The slope of the line \( y = -74x \) is \( -74 \).

The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m \) of the perpendicular line will be:

\[
m = -\frac{1}{-74} = \frac{1}{74}
\]

Now we will 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 the line passes through and \( m \) is the slope. Plugging in our point \( (-7, 5) \) and the slope \( \frac{1}{74} \):

\[
y - 5 = \frac{1}{74}(x + 7)
\]

Now we can find the y-intercept by simplifying this equation.

1. Multiply both sides by 74 to eliminate the fraction:

\[
74(y - 5) = x + 7
\]
\[
74y - 370 = x + 7
\]

2. Rearranging gives us:

\[
74y = x + 377
\]

Now we will express it in slope-intercept form \( y = mx + b \):

\[
y = \frac{1}{74}x + \frac{377}{74}
\]

From this, we can see that the slope is \( \frac{1}{74} \).

Since none of the provided answer choices seem to relate to the actual values we calculated in this way, let's classify the correct response based on the correct slope for the perpendicular line.

Continuing with our choices, we need to identify the slope that is correct and also goes through our point (–7, 5):

Given the problem choices:

- \( y = 47x + 5 \) (Slope: 47)
- \( y = -74x + 5 \) (Slope: -74)
- \( y = -\frac{7}{4}x + 5 \) (Expected Slope: negative, not reciprocal)
- \( y = -\frac{4}{7}x + 1 \) (The slope here does not match correct values.)

The only viable slope for perpendicular based on choices was given by slope \( y=m \) of \( -\frac{7}{4}x\) in reciprocals and \( y \) slope of \( 47x\).

Hence the selection here closely, which would lead us to indicate, under needed values, closely does evaluate could be the valid answer \( y = 47x + 5\) and disregarding other incorrect slopes validated against these checks.

Thus the answer would appear closest among choices appearing proportional to these evaluations, at solid values giving pair arrangements together.

So the answer is:

**Answer:** \( y = 47x + 5 \)