Question

find the equation of the line with slope = 1 that passes through (10,5). write your equation in the form y = mx + b. y =

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m = 1$, so the equation of the line is $y=1\times x + b$, or simply $y=x + b$.

Step2: Substitute the point into the equation

We know that the line passes through the point $(10,5)$. This means that when $x = 10$ and $y = 5$, the equation $y=x + b$ holds. Substitute $x = 10$ and $y = 5$ into $y=x + b$:
\[5=10 + b\]

Step3: Solve for $b$

To solve for $b$, we subtract 10 from both sides of the equation $5 = 10 + b$.
\[b=5 - 10=- 5\]

Step4: Write the final equation

Now that we know $m = 1$ and $b=-5$, substitute these values back into the slope - intercept form $y=mx + b$. We get $y=x-5$.

Answer:

$y = x - 5$