Question

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


A. y = -4x + 1
B. y = -1/2 x + 9
C. y = 4x + 1
D. y = -2x + 9

Answer 1

The general formula for slope-intercept form is
\[y = mx + b\
]Where m is the slope of your line, and b is the value of the y-intercept (the point where x = 0 and where your line crosses the y-axis). With the information you're supplied with is two coordinate points. From this alone, you can find out a few things:

First, you can calculate the slope of the line you're dealing with by plugging it into the slope formula, which is \[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]It doesn't matter which point you choose to represent (x1, y1) or (x2, y2); either will give you the same ultimate result. So plug in first to find for your slope:\[\frac{ (1) - (-1)}{ (4) - (5) } = \frac{ 2 }{ -1 } = -2\]
From here, you have \[y = -2x + b\]
In order to find the y-intercept at this point, just plug into your current equation one of the given points to find out the intercept. For example:\[(-1) = -2(5) + b\]\[-1 = -10 + b\]\[b = 9\]
So all in all, you have \[y = -2x +9\]
Does this make sense?

Answer 2

Whoops, Top part got included into the equation. But this should make sense regardless. Ask if you have any questions.