Write an equation of a line given the slope m = -1/2 and goes through the point (-4, -9). first write the equation in point-slope form, then convert it to slope-intercept form.

Point-slope form looks like this: y - k = m(x - h) where m is the slope and (h, k) are the given coordinates on a line. (h, k) is basically the coordinates (x, y) in disguise, just with different letters to express the formula.

Slope-intercept form looks like this: y = mx + b where m is the slope and b is the given y-intercept.

Using our givens, we can plug them into the formulas to get our final results.

Point-slope form: y - k = m(x - h). The x-value replaces h, the y-value replaces k, and the slope replaces m.
y - (-9) = (-1/2)(x - (-4))
Now we have to use a bit of algebra in order to turn this into slope-intercept form.

y - (-9) = (-1/2)(x - (-4))
y + 9 = (-1/2*x) - (-1/2*-4) Remember that subtracting a negative by a positive is the same thing as adding two positive numbers.
y + 9 = -x/2 + 2 Now we must isolate the y to get slope-intercept form.
y + 9 - 9 = -x/2 + 2 - 9 Don't forget that what you do on one side you must do on the other, so we subtract 9 on the left and right.
y = -x/2 - 7 This is our final result since it is in slope-intercept form (y = mx + b).

I hope this made sense- - if I made anything look confusing please feel free to tell me and I'll do my best to explain!