MHB How Do You Solve Linear Equations with Given Coordinates?

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To solve linear equations using given coordinates, identify the slope (m) by calculating the change in y over the change in x, which is -2 in this case. The linear equation is structured as y = mx + b, where m represents the slope and b is the y-intercept. By substituting known values into the equation, you can solve for b, resulting in the equation y = -2x + 3. Finally, to find specific values, set y to the desired number and solve for x. This method provides a clear approach to determining linear relationships from coordinates.
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Hi Sarahq, and welcome to MHB!

For your Problem 5, you should notice that as $X$ increases by $1$, $Y$ decreases by $2$. So the equation between $X$ and $Y$ should start as $Y = \dfrac{-2}1X \ldots$. You should then be able to find the constant term to complete the equation.
 
Hi Sarahq,

The formula for linear equations is
\[ y = mx+b \]
m = slope and b = shift on the y-axis.

The following formula is used to calculate the slope m
\[ m = \frac{y_2-y_1}{x_2-x_1} \]
(here -2/1 = -2)
Use x-, y-values and m to calculate b:
\[ -23 = -2 * 13 + b \]
solve for b:
\[ -23 = -26 + b | +26 \]
\[ 3 = b \]
so:
\[ y = -2x + 3 \]
Now just set y = 31 and solve for x.
Hope it was helpfull :)
 

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