A line has a slope of 1/2 and passes through the point (6,7). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions... A line has a slope of 1/2 and passes through the point (6,7). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. Solve it.
Understand the Problem
The question is asking for the equation of a line that has a specific slope and passes through a given point. We will use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We can find b by substituting the slope and the point (6,7) into the equation.
Answer
The equation of the line is: $$ y = mx + (7 - 6m) $$
Answer for screen readers
The final equation of the line is:
$$
y = mx + (7 - 6m)
$$
Steps to Solve
-
Identify the slope and point
We are given that the slope $m$ is a specific value (let's assume $m$ for now) and the point is $(6, 7)$. -
Substitute the values into the slope-intercept equation
Using the slope-intercept form $y = mx + b$, we substitute $x = 6$, $y = 7$, and $m$ for the slope. The equation becomes:
$$ 7 = m(6) + b $$ -
Rearranging to solve for the y-intercept (b)
Now, we need to solve for $b$. Rearranging the equation gives:
$$ b = 7 - 6m $$ -
Write the final equation of the line
Substituting $b$ back into the slope-intercept equation gives us:
$$ y = mx + (7 - 6m) $$
This can be written as:
$$ y = mx + 7 - 6m $$
The final equation of the line is:
$$
y = mx + (7 - 6m)
$$
More Information
This equation represents all lines with a given slope $m$ that pass through the point (6, 7). If you know the specific value of $m$, you can substitute it in to find the exact equation of the line.
Tips
- Failing to correctly substitute the values into the equation. Make sure to substitute both $x$ and $y$ correctly.
- Not rearranging the equation properly to isolate $b$. Double-check your algebra when solving for the y-intercept.
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