A line has a slope of 6 and passes through the point (2,7). Write its equation in slope-intercept form.

Question

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of a line in slope-intercept form (which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept), we can use the slope $m=6$ and the point $(2,7)$.

1. Substitute the values into the slope-intercept form: We know the slope $m=6$, so our equation starts as: $$y=6x+b$$

2. Use the point to solve for $b$: Substitute $x=2$ and $y=7$ into the equation: $$7=6(2)+b$$

3. Calculate $6(2)$: $$6(2)=12$$ So, we have: $$7=12+b$$

4. Solve for $b$: $$b=7-12=-5$$

5. Write the final equation: Now that we have $b=-5$, the equation of the line is: $$y=6x-5$$

Thus, the equation of the line in slope-intercept form is: $$\boxed{{\displaystyle y=6x-5}}$$