QuestionWrite an equation for the line that has a slope of $\frac{1}{2}$ and passes through $(6,-3)$ $y=$ Question Help: Video Submit Question

Studdy Solution

STEP 1

1. We need to find the equation of a line.
2. The line has a slope of $\frac{1}{2}$ .
3. The line passes through the point $(6, -3)$ .
4. We will use the point-slope form of a line to find the equation.

STEP 2

1. Recall the point-slope form of a line.
2. Substitute the given slope and point into the point-slope form.
3. Simplify the equation to the slope-intercept form.

STEP 3

Recall the point-slope form of a line, which is given by:
$y - y_1 = m(x - x_1)$
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

STEP 4

Substitute the given slope $m = \frac{1}{2}$ and the point $(6, -3)$ into the point-slope form:
$y - (-3) = \frac{1}{2}(x - 6)$
This simplifies to:
$y + 3 = \frac{1}{2}(x - 6)$

STEP 5

Simplify the equation to the slope-intercept form $y = mx + b$ .
First, distribute the slope $\frac{1}{2}$ on the right side:
$y + 3 = \frac{1}{2}x - \frac{1}{2} \times 6$ $y + 3 = \frac{1}{2}x - 3$
Next, subtract 3 from both sides to solve for $y$ :
$y = \frac{1}{2}x - 3 - 3$ $y = \frac{1}{2}x - 6$
The equation of the line is:
$y = \frac{1}{2}x - 6$

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