Math  /  Algebra

QuestionA line has a slope of 2 and passes through the point (4,4)(-4,-4). Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. \square

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line, specifically in slope-intercept form (y=mx+by = mx + b), given its slope and a point it passes through. Watch out! Remember, slope-intercept form is y=mx+by = mx + b, where mm is the **slope** and bb is the **y-intercept**.
Don't mix these up!

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** is m=2m = 2 and the line passes through the point (4,4)(-4, -4), which means when x=4x = -4, then y=4y = -4.
Let's plug these **values** into the slope-intercept form: y=mx+by = mx + b becomes 4=2(4)+b-4 = 2 \cdot (-4) + b.

STEP 4

Now, let's **solve** for bb, the **y-intercept**.
We have 4=2(4)+b-4 = 2 \cdot (-4) + b.
First, let's simplify the right side: 4=8+b-4 = -8 + b.

STEP 5

To **isolate** bb, we need to add 88 to both sides of the equation.
This is like adding eight to zero on each side, to keep the equation balanced: 4+8=8+b+8-4 + 8 = -8 + b + 8.
This simplifies to 4=b4 = b, so our **y-intercept** is b=4b = 4.

STEP 6

We now have our **slope**, m=2m = 2, and our **y-intercept**, b=4b = 4.
Let's plug these back into the slope-intercept form, y=mx+by = mx + b.

STEP 7

Substituting the **values** gives us the **equation** y=2x+4y = 2x + 4.
And there we have it!

STEP 8

The equation of the line in slope-intercept form is y=2x+4y = 2x + 4.

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