Hey there! :)
We're very simply trying to find the slope-intercept form of an equation of the line that passes through (3, 4) & (1, 0).
In order to find the equation, we must first know what slope-intercept form is.
Slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept
First, we'd need to find the slope of this line. To find the slope, let's use the slope formula.
Slope formula : m = y₂-y₁ / x₂-x₁
Now, simply plug everything in!
Remember : we're plugging in (3, 4) & (1, 0).
m = (0 - 4) / (1 - 3)
Simplify.
m = -4 / -2
Simplify.
m = 2
SO, our slope for this equation is 2.
Now that we know the slope, we can very simply find the y-intercept (which is needed for the slope-intercept form) by using the slope-intercept equation.
Let's use these coordinates : (3, 4)
y = mx + b
Plug our known variables in.
(4) = (2)(3) + b
Simplify.
4 = 6 + b
Subtract 6 from both sides.
4 - 6 = b
Simplify.
-2 = b
So, our slope intercept is -2!
Keep in mind that our slope is 2.
So, now that we have those needed variable knowns, we now can plug our slope and y-intercept into our slope-intercept form equation!
y = mx + b
Plug everything in.
y = 2x - 2
So, our answer is : the third choice, which is y=2x - 2
~Hope I helped!~
