Questions: Write an equation of the line that passes through (-2,2) and is parallel to the line defined by 3x + y = 3. Write the answer in slope-intercept form (if possible) and in standard form (Ax + By = C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.

Write an equation of the line that passes through (-2,2) and is parallel to the line defined by 3x + y = 3. Write the answer in slope-intercept form (if possible) and in standard form (Ax + By = C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.

Transcript text: Write an equation of the line that passes through ( $-2,2)$ and is parallel to the line defined by $3 x+y=3$. Write the answer in slope-intercept form (if possible) and in standard form $(A x+B y=C)$ with smallest integer coefficients. Use the "Cannot be written" button, if applicable. Part: $0 / 2$

Solution

Solution Steps

Step 1: Find the Slope of the Given Line

To find the slope of the line parallel to the given line 3x + y = 3, we first rearrange it into slope-intercept form. The slope $m = -\frac{3}{1}$ is calculated to be -3.

Step 2: Write the Equation of the New Line Using the Point-Slope Form

Using the point $(-2, 2)$ and the slope -3, the point-slope form is $y - 2 = -3(x + 2)$. Rearranging to slope-intercept form gives $y = -3.0x - 4$.

Step 3: Convert to Standard Form

To convert to standard form, we start from the slope-intercept form $y = -3.0x - 4$ and rearrange to get $-3x + (-1)y = -4$, ensuring the coefficients are the smallest set of integers possible.