Answer :
To determine the equation of the line passing through the points [tex]\((44, 6)\)[/tex] and [tex]\((-4, -6)\)[/tex], follow these steps:
1. Calculate the slope (m):
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points [tex]\((44, 6)\)[/tex] and [tex]\((-4, -6)\)[/tex]:
[tex]\[
m = \frac{-6 - 6}{-4 - 44} = \frac{-12}{-48} = \frac{1}{4}
\][/tex]
2. Calculate the y-intercept (b):
The equation of the line in slope-intercept form is [tex]\(y = mx + b\)[/tex]. We can use one of the points and the slope to find [tex]\(b\)[/tex]. Let's use the point [tex]\((44, 6)\)[/tex]:
[tex]\[
6 = \left(\frac{1}{4}\right)(44) + b
\][/tex]
Simplify and solve for [tex]\(b\)[/tex]:
[tex]\[
6 = 11 + b \\
b = 6 - 11 \\
b = -5
\][/tex]
3. Write the equation of the line:
Now that we have both the slope and y-intercept, we can write the equation of the line as:
[tex]\[
y = \frac{1}{4}x - 5
\][/tex]
So, the equation of the line passing through the points [tex]\((44, 6)\)[/tex] and [tex]\((-4, -6)\)[/tex] is:
[tex]\[
y = \frac{1}{4}x - 5
\][/tex]
1. Calculate the slope (m):
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points [tex]\((44, 6)\)[/tex] and [tex]\((-4, -6)\)[/tex]:
[tex]\[
m = \frac{-6 - 6}{-4 - 44} = \frac{-12}{-48} = \frac{1}{4}
\][/tex]
2. Calculate the y-intercept (b):
The equation of the line in slope-intercept form is [tex]\(y = mx + b\)[/tex]. We can use one of the points and the slope to find [tex]\(b\)[/tex]. Let's use the point [tex]\((44, 6)\)[/tex]:
[tex]\[
6 = \left(\frac{1}{4}\right)(44) + b
\][/tex]
Simplify and solve for [tex]\(b\)[/tex]:
[tex]\[
6 = 11 + b \\
b = 6 - 11 \\
b = -5
\][/tex]
3. Write the equation of the line:
Now that we have both the slope and y-intercept, we can write the equation of the line as:
[tex]\[
y = \frac{1}{4}x - 5
\][/tex]
So, the equation of the line passing through the points [tex]\((44, 6)\)[/tex] and [tex]\((-4, -6)\)[/tex] is:
[tex]\[
y = \frac{1}{4}x - 5
\][/tex]
