Question

Write a linear equation that passes through the points(2,-2) and (0,1)

Answer 1

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

m = 1 - (-2)/0 - (2)

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer 2

Answer:

$y=\frac{-3}{2}x-1$

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

$\frac{y_2-y_1}{x_2-x_1}=m$

Plug in what we know

$\frac{(1)-(-2)}{0-2}=m$

$m=\frac{-3}{2}$

$y=\frac{-3}{2}x-b$

Plug in one of the points given and solve to find our y-intercept [b]

$-2=\frac{-3}{2}(2)-b$

$b=1$

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

$y=\frac{-3}{2}x-1$