Question

a line has a slope of 1 and passes through the point (6, 10). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall 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 $m = 1$ and the line passes through the point $(x,y)=(6,10)$.

Step2: Substitute values into the equation

Substitute $m = 1$, $x = 6$ and $y = 10$ into $y=mx + b$. So we have $10=1\times6 + b$.

Step3: Solve for $b$

Simplify the right - hand side of the equation: $10 = 6 + b$. Subtract 6 from both sides of the equation: $b=10 - 6=4$.

Step4: Write the equation

Now that we know $m = 1$ and $b = 4$, substitute these values back into the slope - intercept form $y=mx + b$. We get $y=x + 4$.

Answer:

$y = x+4$