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Math  /  Algebra

QuestionWrite the equation of the line that passes through the point (−4,−9)(-4,-9) and has a slope of 12\frac{1}{2}

Studdy Solution

STEP 1

1. We are given a point (−4,−9)(-4, -9) and a slope m=12m = \frac{1}{2}.
2. We need to find the equation of a line in the slope-intercept form y=mx+by = mx + b.
3. The slope-intercept form requires a slope mm and a y-intercept bb.

STEP 2

1. Understand the slope-intercept form of a line.
2. Use the given point and slope to find the y-intercept bb.
3. Write the equation of the line.

STEP 3

The slope-intercept form of a line is given by:
y=mx+b y = mx + b
where mm is the slope and bb is the y-intercept.

STEP 4

We are given the slope m=12m = \frac{1}{2} and a point (−4,−9)(-4, -9). We can substitute these values into the slope-intercept form to solve for bb.
Substitute x=−4x = -4, y=−9y = -9, and m=12m = \frac{1}{2} into the equation:
−9=12(−4)+b -9 = \frac{1}{2}(-4) + b

STEP 5

Simplify the equation to find bb:
−9=−2+b -9 = -2 + b
Add 2 to both sides to solve for bb:
b=−9+2 b = -9 + 2
b=−7 b = -7

STEP 6

Now that we have m=12m = \frac{1}{2} and b=−7b = -7, we can write the equation of the line:
y=12x−7 y = \frac{1}{2}x - 7
The equation of the line is:
y=12x−7 \boxed{y = \frac{1}{2}x - 7}

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