# Write an equation of the line that passes through the given points.

(-1,5) and (2,-7)

The equation is ___.

Here's what, I did:

Slope = rise/run = y2 - y1/ x2 - x1, where x2 - x1 # 0

Substitute the coordinates of the points into this formula and simplify.

slope = -7 -5/2-(-1)
= 3

Then use the slope and the coordinates of one of the points to find N. For this problem, use the slope and the first given point.
y = mx + B
5 = 3(-1) + b
4 = B

Finally, substitute the slope and y intercept into the slope intercept form.
y = mx + b
y = 3x + 5

Therefore the answer is y= 3x + 5

Please correct me if this is wrong.

## clearly you did not check your answer. The two points must be on the line.

(-1,5): does 3(-1) + 5 = 5? No❌
(2,-7): does 3(2)-5 = -7? No ❌

You say slope = -7 -5/2-(-1) = 3
But slope = (-7 -5)/(2-(-1)) = -12/3 = -4
So you know y = -4x + b
Now use one of the points to find b.

## Why did the mathematician break up with the graphing calculator?

Because it wasn't rational enough and kept drawing imaginary lines!

## Your approach is correct! Let's go through the steps together:

Step 1: Find the slope.
Using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, 5) and (x2, y2) = (2, -7)
slope = (-7 - 5) / (2 - (-1))
slope = -12 / 3
slope = -4

Step 2: Use the slope and one point to find the y-intercept.
Using the slope-intercept form: y = mx + b, where m is the slope and (x, y) is the given point.
We'll use the first point (-1, 5):
5 = -4(-1) + b
5 = 4 + b
b = 5 - 4
b = 1

Step 3: Substitute the slope and y-intercept into the equation.
The equation becomes:
y = -4x + 1

So, after going through the steps, the equation of the line that passes through the points (-1,5) and (2,-7) is y = -4x + 1.