To find the equation of a line given two anchor points, [tex]\((-4, -36)\)[/tex] and [tex]\( (6, 54)\)[/tex], follow these steps:
1. Determine the slope ([tex]\(m\)[/tex]) of the line:
The formula to calculate the slope [tex]\(m\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Using the coordinates [tex]\((x_1, y_1) = (-4, -36)\)[/tex] and [tex]\((x_2, y_2) = (6, 54)\)[/tex], plug in the values:
[tex]\[
m = \frac{54 - (-36)}{6 - (-4)} = \frac{54 + 36}{6 + 4} = \frac{90}{10} = 9
\][/tex]
2. Calculate the y-intercept ([tex]\(b\)[/tex]):
Use the slope-intercept form of the equation of a line:
[tex]\[
y = mx + b
\][/tex]
Substitute one of the points and the slope into the equation to solve for [tex]\(b\)[/tex]. We'll use the point [tex]\((-4, -36)\)[/tex]:
[tex]\[
-36 = 9(-4) + b
\][/tex]
Simplify the equation:
[tex]\[
-36 = -36 + b
\][/tex]
Solving for [tex]\(b\)[/tex] gives:
[tex]\[
b = 0
\][/tex]
3. Write the equation of the line:
Now that we have the slope [tex]\(m = 9\)[/tex] and the y-intercept [tex]\(b = 0\)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[
y = 9x + 0
\][/tex]
Simplifying further:
[tex]\[
y = 9x
\][/tex]
Therefore, the equation of the line is [tex]\(y = 9x\)[/tex].
