Questions: The equation of a line is given below. -3 x+2 y=-2 Find the slope and the y-intercept. Then use them to graph the line. slope: y-intercept:

Transcript text: The equation of a line is given below. \[ -3 x+2 y=-2 \] Find the slope and the $y$-intercept. Then use them to graph the line. slope: $\square$ $y$-intercept: $\square$

Solution

Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The given equation is: \[ -3x + 2y = -2 \] To find the slope and the $y$-intercept, we need to rewrite this equation in the slope-intercept form, $y = mx + b$.

Step 2: Solve for $y$

Add $3x$ to both sides: \[ 2y = 3x - 2 \] Divide every term by 2: \[ y = \frac{3}{2}x - 1 \]

Step 3: Identify the slope and $y$-intercept

From the equation $y = \frac{3}{2}x - 1$, we can identify:

The slope $m$ is $\frac{3}{2}$.
The $y$-intercept $b$ is $-1$.

Final Answer

Slope: $\frac{3}{2}$
$y$-intercept: $-1$

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = (3/2)x - 1"], "latex_expressions": ["$y = \\frac{3}{2}x - 1$"]}

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