QuestionDetermine the slope and $y$ -intercept of the line given by the equation $6x - 2y = 3$ .

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as $6x -y =3$ . The equation is in the standard form $Ax + By = C$
3. We need to convert this equation to slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the $y$ -intercept.

STEP 2

To convert the equation to slope-intercept form, we need to isolate $y$ . Start by subtracting $6x$ from both sides of the equation.
$-2y = -6x +$

STEP 3

Next, divide every term by $-2$ to solve for $y$ .
$y =3x - \frac{3}{2}$

STEP 4

Now, the equation is in the slope-intercept form. We can identify the slope and the $y$ -intercept from the equation.
The slope $m$ is the coefficient of $x$ , and the $y$ -intercept $b$ is the constant term.
So, the slope $m =3$ and the $y$ -intercept $b = -\frac{3}{2}$ .
The slope and the $y$ -intercept of the line are $3$ and $-\frac{3}{2}$ , respectively.

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