Write the slope intercept form of the equation of the line that passes through the points...

Write the slope intercept form of the equation of the line that passes through the point (-5, 4) and has a slope of -1.

Please explain. I have had the hardent time trying to understand how to do this.

the equation for a line is y-y1=m(x-x1)

so we take our points and plug it in

y-4=-1(x-(-5))
y-4=-1(x+5)
y-4=-x-5
y=-x-1

Okay so first off, we know that the slope-intercept equation is y = mx + b, with "m" representing the slope and "b" representing the y-intercept.

The slope is given in the problem, which is -1. Plug that in for "m", and you get y = (-1)x + b.

Now, we look at the coordinates that are given. Coordinates are always in the form (x,y), so that means the x-coordinate is -5 and the y-coordinate is 4. Take those, and plug those into the slope-intercept equation. We do that so we can find the y-intercept, which is "b."

Since the coordinates of the point is (-5, 4), plugging that into the equation will look like
4 = (-1)(-5) + b
Multiply (-1) and (-5) and you'll get positive 5.
Next, you divide 4 by 5 so that you can find the value of "b."
4/5 = b

Now you have all of the variables that you need for the equation: y = -1x + 4/5

Since you're given a point and a slope, substitute into the point-slope form of a linear equation first.

point-slope form: y - y1 = m(x - x1) where m = slope, (x1,y1) = point

You get: y - 4 = -1(x - (-5)) ===> y - 4 = -1(x + 5)

Now use algebra to convert to slope-intercept form (y = mx + b).

y - 4 = -1(x + 5) ===> y - 4 = -x - 5 ===> y = -x - 1

Slope-intercept form of a line is usually expressed as y = mx + b. m is the slope of the line and b is the y-intercept. Given a point and the slope, a common approach is to start in point-slope form and then solve for y and simplify to get slope-intercept form.