Indicate in standard form the equation of the line passing through the given points, in the equation box below. A(4, 1), B(5, 2)

Question

equation for standered form Ax+By=C

Answer 1

line through (4,1), (5,2) has slope = (2-1)/(5-4) = 1/1 = 1 = m

y=mx+ b = x+ b, solve for b by plugging in either point

1=1(4) + b

b = 1-4 = -3

y=x-3

x-y = 3

Ax + By = 3 where A=1, B=-1 and C = 3

Answer 2

To find the equation of a line, you can start by finding the slope. Use the two given points to find the slope. The slope is the ratio of the change in y-values over the change in x-values.

The two points are (4, 1) and (5, 2), so the change in y-values is 2-1 = 1. The change in x-values is 5-4 = 1. So, the ratio is 1/1. The slope for this line is 1.

Now that you know the slope, you need to find the y-intercept (this is one way to proceed).

The slope-intercept form of all linear equations is y=mx+b. The m is the slope, which we already know is 1.

So we know:

y=1x+b

Temporarily plug in one of the two points for x and y. I will use (4, 1).

1=1(4) +b

1= 4 + b

-3 = b

So, now you know the slope-intercept equation is y=x+-3

You need to change this into Standard Form: Ax + By = C (A, B, C need to be integers. A should be positive).

y = x + -3

y - x = -3

-x + y = -3

x + -y = 3

(That last step is to be sure that the A value is positive.)

Answer 3

First find the equation in point-slope form: y - y1 = m(x-x1), where m is slope and (x1,y1) is point line passes through.

slope between A and B is (2-1)/(5-4) = 1. Using A(4,1) for (x1,y1) we get:

y - 1 = x - 4

convert to standard form by getting x on left side and numbers on right side:

-x + y = -3