Question

What is an equation of the line that passes through the points (−1,7) and (1,−3)?

Answer 1

y = -5x + 2

Explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (−1,7) and (1,−3)

We see the y decrease by 10 and the x increase by 2, so the slope is

m = -10/2 = -5

Y-intercept is located at (0, 2)

So, our equation is y = -5x + 2

Answer 2

y = -5x + 2

Explanation:

General equation: y = mx + b where m is the slope and b is the y-intercept.

To calculate the slope, we can do
`(y_(2)-y_(1) )/(x_(2)-x_(1))`, which would be
`(-3 - 7)/(1-(-1))` = (-10/2) = -5.
To calculate the y-intercept, we substitute one of our coordinates into the equation and solve for b.

So far we have y = -5x +b.
Substitute (-1,7):

7 = -5(-1) + b

7 = 5 +b b = 7-5 = 2.
Final Equation: y = -5x + 2.
Check it is correct by substituting in the second coordinate.
y = -5(1) + 2 = -5 + 2 = -3 (correct)