Question

Find the equation of a line that contains the points (4,−1) and (−1,−4). Write the equation in slope-intercept form, using fractions when required.

Answer 1

Answer:

y = 3/5x - 17/5

Step-by-step explanation:

slope formula: (y₂ - y₁) / (x₂ - x₁)

First, plug in these values of the two given points.

(-4 - (-1)) / (-1 - 4)

Simplify within the parentheses.

(-4 + 1) / (-1 - 4)

(-3) / (-5)

3/5

This is your slope. Plug this into a standard slope-intercept equation: y = mx + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (-1, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = 3/5(-1) + b

Multiply.

-4 = -3/5 + b

Add 3/5 to both sides. -- To add it easier, convert 4 to a have a denominator of 5.

-20/5 = -3/5 + b

-20/5 + 3/5 = b

-17/5 = b

Now, plug this into your standard equation.

y = 3/5x - 17/5

Check this equation by plugging in the other point you did not use (4, -1)

-1 = 3/5(4) - 17/5

-1 = 12/5 - 17/5

-1 = -5/5

-1 = -1

Your answer is correct!

Hope this helps!