Determine whether the pair of lines is parallel perpendicular, or neither. x+3y=10 3x+9y=18 The lines are square

To determine whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of each line.<br /><br />Step 1: Find the slope of the first line, $x+3y=10$.<br />To find the slope, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope.<br /><br />$x + 3y = 10$<br />$3y = -x + 10$<br />$y = -\frac{1}{3}x + \frac{10}{3}$<br /><br />The slope of the first line is $-\frac{1}{3}$.<br /><br />Step 2: Find the slope of the second line, $3x+9y=18$.<br />Again, we need to rewrite the equation in slope-intercept form.<br /><br />$3x + 9y = 18$<br />$9y = -3x + 18$<br />$y = -\frac{1}{3}x + 2$<br /><br />The slope of the second line is also $-\frac{1}{3}$.<br /><br />Step 3: Compare the slopes of the two lines.<br />If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. If neither condition is met, the lines are neither parallel nor perpendicular.<br /><br />In this case, both lines have the same slope of $-\frac{1}{3}$, so the lines are parallel.<br /><br />Answer: The lines are parallel.