Question

Write the equation of a line that goes through the points (1, 4) and (2, 2)

Answer 1

first get your gradient by finding rise over run (y1-y2)/(x1-x2)

Answer 2

gradient is equivalent to the slope of the line

Answer 3

first find the gradient then use the gradient to find the equation of line with any pair of coordinate given

Answer 4

how

Answer 5

A line is defined as:
y = mx + b

where:
m = slope / gradient
b = y-intercept

So find m and b such that they fit the description.

Answer 6

so how

Answer 7

A point on a graph is denoted (x, y) such that x is a point x units along the x-axis and y is a point y units along the y-axis.

If you have a point (1, 4) and (2, 2) then you know that for x = 1, y = 4, and for x = 2, y = 2.

So find an equation that satisfies those conditions.

Here's how you find the slope:
slope = rise / run
=> m = dy / dx

where dy = change in y-coordinates from point A to point B
and dx = change in x-coordinates from point A to point B

Answer 8

?

Answer 9

Do you know what Cartesian geometry is?

Answer 10

so x=1 and y=4 in the first point. On a graph x coordinates will move the point left or rioght and the y coordinates will move the point up or down. The first step to making an equation is to find the slope (How much the point has gone up or down divided by how much the point has gone left or right.)

Answer 11

So from X=1 to X=2 we move right +1 on the graph. The run is +1

Answer 12

from Y=4 to Y=2 we move down -2 so the rise is -2.

Answer 13

Put them together for the slope. Rise/Run = 1/-2 or -1/2

Answer 14

Now that we know the slope we need to find the y-intercept. Where the line crosses the y axis

Answer 15

I did the slope backwards :3 It's actually -2/1 or just -2

Answer 16

Y=2 at X=1 so what will Y be at X=0? Use the slope and trace the line back from (1,4). You should reach (0,6).

Answer 17

Now to make the equation. y = mx + b where m is the slope and b is the y-intercept

Answer 18

m=-2 and b=+6 so your equation comes out to be y = -2x + 6

Answer 19

And that's how math gud.