Final answer:
To find the slope-intercept equation of a line that has a slope of -34 and passes through the point (-4, 6), use the form y = mx + b. After plugging the values into the equation, we determine that the y-intercept, b, is -130. Therefore, the equation of the line is y = -34x - 130.
Step-by-step explanation:
To find the slope-intercept equation of a line that passes through the point (-4, 6) with a given slope of -34, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. By plugging in our slope and the coordinates of the given point into the equation, we can solve for b.
Starting with the slope-intercept form, we put in our known values:
y = -34x + b
Next, we substitute the coordinates of our given point (-4, 6):
6 = -34(-4) + b
Now we calculate to find the value of b:
6 = 136 + b
This simplifies to b = 6 - 136, which gives us b = -130.
Thus, the slope-intercept equation for the line is:
y = -34x - 130