Math  /  Algebra

QuestionA line passes through the point (10,1)(10,1) and has a slope of 12\frac{1}{2}. Write an equation in slope-intercept form for this line. \square

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line, specifically in *slope-intercept form*, given a point it passes through and its slope. Watch out! Don't mix up the *x* and *y* coordinates of the given point!
Also, remember slope-intercept form is y=mx+by = mx + b, not x=my+bx = my + b.

STEP 2

1. Plug in the known values
2. Solve for the y-intercept
3. Write the final equation

STEP 3

We know the **slope-intercept form** of a linear equation is y=mx+by = mx + b, where mm is the **slope** and bb is the **y-intercept**.
We're given that the slope mm is 12\frac{1}{2}, and the line passes through the point (10,1)(10, 1), which means when x=10x = 10, y=1y = 1.
Let's **plug these values** into our equation!

STEP 4

Substituting the given values, we get 1=1210+b1 = \frac{1}{2} \cdot 10 + b.
See how we replaced yy with **1**, mm with 12\frac{\textbf{1}}{\textbf{2}}, and xx with **10**?
Now we just need to solve for bb, the **y-intercept**!

STEP 5

Let's **simplify** the equation 1=1210+b1 = \frac{1}{2} \cdot 10 + b.
First, we multiply 12\frac{1}{2} by 10.
Remember, multiplying by 12\frac{1}{2} is the same as dividing by 2, so 1210=102=5\frac{1}{2} \cdot 10 = \frac{10}{2} = 5.

STEP 6

Now our equation looks like 1=5+b1 = 5 + b.
To **isolate** bb, we need to get rid of the 5 on the right side.
We can do this by adding 5-5 to *both* sides of the equation: 1+(5)=5+b+(5)1 + (-5) = 5 + b + (-5).

STEP 7

Simplifying both sides gives us 4=b-4 = b.
Awesome! We found our **y-intercept**: b=4b = -4.

STEP 8

Now that we have our **slope** m=12m = \frac{1}{2} and our **y-intercept** b=4b = -4, we can **plug them back** into the slope-intercept form: y=mx+by = mx + b.

STEP 9

Substituting the values, we get y=12x+(4)y = \frac{1}{2}x + (-4), which simplifies to y=12x4y = \frac{1}{2}x - 4.
This is our **final equation** in slope-intercept form!

STEP 10

The equation of the line in slope-intercept form is y=12x4y = \frac{1}{2}x - 4.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord