What is the equation of the line between #(-9,16)# and #(4,2)#?

Question

Hazel Anglin · Accepted Answer

#14x+13y=82#

Equation of the line involves:

finding the gradient 2)using the point gradient formula to find your equation (in this case, this the second step)

#Gradient (m)=(16-2)/(-9-4)# = #14/-13#

Equation of line:

We also using the point #(4,2)#

#(y-2)=-14/13(x-4)#

#13y-26=-14x+56#

#14x+13y=82#

Jace Anderson · Answer

undefined To find the equation of the line passing through the points (-9,16) and (4,2), we first need to determine the slope (m) of the line using the formula:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Using the coordinates of the two points:

$$ m = \frac{{2 - 16}}{{4 - (-9)}} $$
$$ m = \frac{{-14}}{{4 + 9}} $$
$$ m = \frac{{-14}}{{13}} $$

Now that we have the slope (m), we can use the point-slope form of the equation of a line, which is:

$$ y - y_1 = m(x - x_1) $$

We can choose either point (-9,16) or (4,2) to plug into the equation. Let's use (-9,16):

$$ y - 16 = \frac{{-14}}{{13}}(x - (-9)) $$
$$ y - 16 = \frac{{-14}}{{13}}(x + 9) $$

Now, we can simplify the equation:

$$ y - 16 = \frac{{-14}}{{13}}x - \frac{{14 \cdot 9}}{{13}} $$
$$ y - 16 = \frac{{-14}}{{13}}x - \frac{{126}}{{13}} $$

Adding 16 to both sides:

$$ y = \frac{{-14}}{{13}}x - \frac{{126}}{{13}} + 16 $$
$$ y = \frac{{-14}}{{13}}x - \frac{{126}}{{13}} + \frac{{208}}{{13}} $$
$$ y = \frac{{-14}}{{13}}x + \frac{{82}}{{13}} $$

So, the equation of the line passing through the points (-9,16) and (4,2) is $ y = -\frac{{14}}{{13}}x + \frac{{82}}{{13}} $.

Ethan Adkins · Answer

undefined To find the equation of the line passing through the points (-9, 16) and (4, 2), we can use the point-slope form of a linear equation, which is:

$y - y_1 = m(x - x_1)$

Where:
$m$ is the slope of the line, and
$(x_1, y_1)$ is one of the given points.

First, let's find the slope ($m$):
$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Given points:
$(x_1, y_1) = (-9, 16)$
$(x_2, y_2) = (4, 2)$

Now, calculate the slope:
$m = \frac{{2 - 16}}{{4 - (-9)}}$
$m = \frac{{-14}}{{13}}$

Now that we have the slope, we can choose either point (-9, 16) or (4, 2) and substitute into the point-slope form to find the equation. Let's use point (-9, 16):

$y - 16 = \frac{{-14}}{{13}}(x - (-9))$
$y - 16 = \frac{{-14}}{{13}}(x + 9)$

Expanding and simplifying:
$y - 16 = \frac{{-14}}{{13}}x - \frac{{126}}{{13}}$
$y = \frac{{-14}}{{13}}x + \frac{{210}}{{13}}$

So, the equation of the line passing through the points (-9, 16) and (4, 2) is $y = -\frac{{14}}{{13}}x + \frac{{210}}{{13}}$.