Question What is an equation of the line that passes through the point (-8,-4) and is parallel to the line x-y=2 Answer Attemptiout of 2 square

To find the equation of the line that passes through the point $(-8,-4)$ and is parallel to the line $x-y=2$, we need to follow these steps:<br /><br />1. Determine the slope of the given line $x-y=2$.<br />2. Use the slope to write the equation of the parallel line.<br />3. Substitute the given point into the equation to find the y-intercept.<br /><br />Step 1: Determine the slope of the given line $x-y=2$.<br />The given line can be rewritten in slope-intercept form as $y = x - 2$. The slope of this line is 1.<br /><br />Step 2: Use the slope to write the equation of the parallel line.<br />Since the parallel line has the same slope as the given line, the slope of the parallel line is also 1. We can use the point-slope form of a linear equation to write the equation of the parallel line:<br />$y - y_1 = m(x - x_1)$<br />where $(x_1, y_1)$ is the given point $(-8,-4)$ and $m$ is the slope.<br /><br />Substituting the values, we get:<br />$y - (-4) = 1(x - (-8))$<br />$y + 4 = x + 8$<br />$y = x + 4$<br /><br />Step 3: Substitute the given point into the equation to find the y-intercept.<br />Substituting the point $(-8,-4)$ into the equation $y = x + 4$, we get:<br />$-4 = -8 + 4$<br />$-4 = -4$<br /><br />The equation of the line that passes through the point $(-8,-4)$ and is parallel to the line $x-y=2$ is $y = x + 4$.