To find the equation of a line in slope-intercept form ([tex]\(y = mx + b\)[/tex]), we need two key pieces of information: the slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(b\)[/tex]).
Given:
- The line passes through the point [tex]\((-1, -8)\)[/tex]
- The slope ([tex]\(m\)[/tex]) is [tex]\(-7\)[/tex]
We start by substituting the slope and the coordinates of the given point into the slope-intercept form equation to find the y-intercept ([tex]\(b\)[/tex]).
The general equation of a line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]
Substitute the slope [tex]\(-7\)[/tex] for [tex]\(m\)[/tex] and the coordinates of the point [tex]\((-1, -8)\)[/tex] for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ -8 = (-7)(-1) + b \][/tex]
Simplify the equation:
[tex]\[ -8 = 7 + b \][/tex]
To isolate [tex]\(b\)[/tex], subtract 7 from both sides:
[tex]\[ b = -8 - 7 \][/tex]
[tex]\[ b = -15 \][/tex]
Now, we have the slope ([tex]\(m = -7\)[/tex]) and the y-intercept ([tex]\(b = -15\)[/tex]). We can write the equation of the line in slope-intercept form:
[tex]\[ y = -7x - 15 \][/tex]
Therefore, our equation is:
[tex]\[ y = -7x - 15 \][/tex]
