Here's a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form

y = -2x - 4

Step-by-step explanation:

Step 1: Find slope m

m = (-4 - 0)/(0 + 2)

m = -4/2

m = -2

y = -2x + b

Step 2: Find b

*Since we are given the y-intercept (0, -4) our b = -4

y = -2x - 4

Step-by-step explanation:

Slope-intercept form is y = mx + b where m is the slope of the line and b is where the line goes through the y-axis. We'll find b first, since that's the easiest. The graph of the line goes through the y-axis at (0, -4), so b = -4.

Now for the slope. First of all, note that the graph is going from upper left to lower right. This indicates that the slope is negative. If it was going from lower left to upper right, the slope would be positive. Ours is negative, so when we use the rise over the run to "count" the slope, we better end up with a negative number!

Locate now where the line goes through the x-axis. That point is (-2, 0). That's called the x-intercept. From that point to the y-intercept of (0, -4), we have to go 4 units down and 2 units to the right. Going down or left indicates negative movement, while going up or right indicates positive. If we go down 4, that's -4; if we go right 2, that +2. Slope, being rise over run, looks like this for us: -4/2, which is -2. The slope came out negative, so we can write the equation now.

m = -2 and b = -4

y =  mx + b becomes

y = -2x - 4

**Just because the formula says "..+ b" doesn't mean that it HAS to be a +. Remember that "plus a minus" is another way of writing subtraction. So your slope-intercept equation COULD ALSO be written as y = -2x + (-4) and that would also be correct.**

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