Answer:
To find the equation of a line that passes through a given point and has a specific slope, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of the given point, m represents the slope of the line, and (x, y) represents any other point on the line.
In this case, the given point is (-2, -8), and the slope is 11. Substituting these values into the point-slope form, we get:
y - (-8) = 11(x - (-2))
Simplifying further:
y + 8 = 11(x + 2)
Expanding the brackets:
y + 8 = 11x + 22
Now, let's rearrange the equation to obtain the slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept:
y = 11x + 22 - 8
Simplifying further:
y = 11x + 14
Therefore, the equation of the line that passes through the point (-2, -8) with a slope of 11 is y = 11x + 14.
Explanation: