Question

Write an equation in slope-intercept form for the line that passes through (1,9), and (3,5).

Answer 1

To write the equation of the line, we will use the point-slope formula.

To do this, we need a point and a slope.

We can find out slope by using the slope formula.

m = y₂ - y₁ / x₂ - x₁

So we have 5 - 9 / 3 - 1 or -4/2 which is -2.

Now let's use the point-slope formula.

y - y₁ = m(x - x₁)

Now substitute one of our points (x₁, y₁) into our formula.

So we have y - 5 = -2(x - 3).

Distributing the -2 gives us y - 5 = -2x + 6.

Moving the -5 to the right, we have y = -2x + 11.

So y = -2x + 11 is our equation.

Answer 2

So first find the slope using the two given points (1,9), (3,5).

Use a formula: y2-y1/x2-x1 aka rise/run

So that makes it 5-9/3-1 = -4/2 = -2

Then you can plug in one of the given points and the slope you just found into the slope-intercept form equation.

Slope intercept form: y=mx + b
Plug in the points: (3,5) and slope - 2
5=-2(3) + b
5=-6+b
11=b
Now that we have our y intercept and our slope who can write the equation in slope-intercept form
Y = -2x + 11
This is the equation of the line. You can check it by plugging in the points given and seeing If it works

Good luck! :)