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liberstina [14]
2 years ago
7

Write the equation of a line in slope intercept form that passes through the two points. 4,-1 and 6,-7

Mathematics
1 answer:
Arlecino [84]2 years ago
8 0

A line has an equation of,

y=mx+n.

m is called a slope

n is called y-intercept

We are also given two points (x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7).

We begin with computing the slope,

m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}

We have computed the slope m and our equation is almost done,

y=-3x+n

Next step is to find out what y-intercept n is. I will use point (4,-1) and insert x and y it into already known equation, then solve for n,

-1=-3(4)+n

-1=-12+n\implies n=\boxed{11}

The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,

\boxed{y=-3x+11}

Hope this helps. :)

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