Find the equation for (191,149) and (231,180)

Question

This is for a major project I have any help would be amazing I’m so confused rn

Answer 1

Anssumng you are needing the equation of the line passing through these two points (accuracy of question helps), start with two-point form (Algeba 1)

(y - 149) / (x - 191) = (180 - 149) / (231 - 191)

Answer 2

Hello, Hailey,

The question is slightly ambiguous, so don't think that you are the only one that is confused. To even start, we need to make two assumptions:

1) The question wants us to find an equation that will intersect both points, and

2) The equation is linear. We are only given two points, so we can't assume anything else with the data provided.

Given these assumptions, let's look for an equation of the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0). We need to start with the slope.

The slope of a line, m, is the change of y per a change in x. It is sometimes called the "Rise/Run." Calculate both the Rise and Run going from point (191,149) to (231,180):

Rise: (180 - 149) = 31

Run: (231 - 191) = 40

The slope, m is the Rise/Run: (31/40), or 0.775

The equation becomes y = (0.775)x + b

We need to find a value of b that foces the line to intersect both points. This is easily done using either of the two given points. I use (191,149):

y = (0.775)x + b

149 = (0.775)*(191) + b for (191,149)

149 = (148.025) + b

b = 0.975

The equation becomes y = (0.775)x + (0.975)

This equation will produce a line that intersects both the given points. Try the free DESMOS online graphing utility to see the result. (It was too large to post here).