Consider the line

=y+76x2
.
Find the equation of the line that is parallel to this line and passes through the point
, −7 4
.

Find the equation of the line that is perpendicular to this line and passes through the point
, −7 4
.

You want to try that equation again?

=y+76x2

makes no sense.

straight lines are usually written in the form

y = mx + b,
e.g. : y = 5x - 9

yours looks nothing like that

furthermore, points are shown in the form (-7,4)

repost so we know what you mean

To find the equation of the line that is parallel to the given line and passes through the point (-7, 4), we need to determine the slope of the given line and use it to construct the equation of the parallel line.

The equation of a line is typically written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

The given line is in the form "= y + 76x^2." Let's rewrite it in the standard form:

y = -76x^2

Comparing this equation to the standard form, we see that the slope of the given line is 0. This means that any line parallel to it will also have a slope of 0.

Since the slope is 0, the equation of the parallel line passing through (-7, 4) will be in the form y = b, where b represents the y-coordinate of the point through which the line passes.

Therefore, the equation of the line parallel to the given line and passing through (-7, 4) is y = 4.

To find the equation of the line that is perpendicular to the given line and passes through the point (-7, 4), we again need to determine the slope of the given line and use it to construct the equation of the perpendicular line.

The slope of the given line can be determined by finding the derivative of the equation with respect to x. Taking the derivative of -76x^2 gives us -152x.

The slope of a line perpendicular to the given line is the negative reciprocal of the slope (-152x). Let's denote this slope as m1.

To find the negative reciprocal of -152x, we invert it and change the sign:

m1 = -1/(-152x) = 1/(152x)

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through (-7, 4) as follows:

y - 4 = m1(x + 7)

Substituting the value of m1, we get:

y - 4 = (1/(152x))(x + 7)

Simplifying and rearranging, we have:

y - 4 = (1/152)(x + 7)

Multiplying through by 152 to eliminate the fraction:

152y - 608 = x + 7

Finally, rearranging the equation to express y as a function of x:

y = (1/152)x - 601/152

So, the equation of the line that is perpendicular to the given line and passes through the point (-7, 4) is y = (1/152)x - 601/152.