Question

A line contains the point (2, 5) and has a slope of −4.

What is the equation of the line in slope-intercept form?

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y = __ x +__

Answer 1

Answer is

To find y intercept using point (2, 5)
Formula y - y1 = m (x -x1)

y - 5 = -4 (x - 2)
Distribute

y -5 = -4x + 8
add 5 to both sides to isolate y

y -5 +5 = -4x + 8 + 5
Simplify

y = -4x + 13

See line on graph as it contains the point (2,5) and crosses the y axis at 13.

Answer 2

y = -4x + 13

Explanation:

y = mx + b

We need the slope (m) which was given to us: -4

We need to find the y-intercept (b)

We will use the point given (2,5) and the slope to find b.

y = 5 from the point (2,5)

x = 2 from the point (2,5)

m = -4 given

substitute these into the equation

y =mx + b

5 = (-4)2 + b

5 = -8 + b Add 8 to both sides

5 + 8 = -8 + 8 + b

13 = b

We now know that m is -4 and b is 13. Write the equation

y = mx + b

y = -4x + 13