Final answer:
To write the equation of the line with a slope of -5/4 that passes through the point (-8, 2), we use the slope-intercept form y = mx + b. Substituting the slope and point into the equation and solving for b gives us b = -8. Hence, the equation of the line is y = -5/4x - 8.
Step-by-step explanation:
To write an equation of a line in slope-intercept form, which is y = mx + b, we need the slope (m) and the y-intercept (b). Given that the line has a slope of -5/4 and passes through the point (-8, 2), we can plug the slope and the point into the slope-intercept form to find b.
The slope-intercept form is derived from the definition of a slope, which is the rise over the run, and visually represents the line's rate of change on a graph. For any point (x, y) on the line, the change in y divided by the change in x from another point on the line will consistently equal the slope. Therefore, to find the y-intercept, we can rearrange the equation to b = y - mx and substitute the values of the given point:
b = 2 - (-5/4)(-8)
Solving for b, we get:
b = 2 - (5/4) × 8
b = 2 - 10
b = -8
Having both the slope and the y-intercept, the equation of the line in slope-intercept form is:
y = -5/4x - 8