<p>How do you solve this?</p>
<p>In the xy plane, line L is the graph of 2x + by = 3, where b is a constant. The graph of 2x +10y = 5 is parallel to line L. What is the value of b?</p>
<p>Parallel lines are lines that have the same slope.</p>
<p>Solving the first line for y = mx + b form, you get:</p>
<p>by = -2x + 3</p>
<p>y = (-2/b)x + (3/b)</p>
<p>Hence, the slope of the first line is -2/b.</p>
<p>Solving the second line for y = mx + b form, you get:</p>
<p>10y = -2x + 5</p>
<p>y = (-1/5)x + 1/2</p>
<p>Hence, the slope of the second line is -1/5.</p>
<p>Setting these slopes equal: </p>
<p>-2/b = -1/5</p>
<p>-b = -10</p>
<p>b = 10</p>
<p>Thank you.</p>
<p>Faster: for all lines with equations in the form Ax + By = C, m = (-A/B). Since these two lines have the same slope (because they are parallel), and the same value for A (that is, A = 2), they must also have the same value for B.</p>
<p>^ That is indeed faster, but I’ve found that standard form makes less sense than slope-intercept form to most students. To each his own, though.</p>
<p>I completely agree. Most high school students do think almost exclusively in slope-intercept form, and that’s the best way to reach them. I didn’t mean to knock your explanation, which was really good. Just wanted to offer another way of looking at it, since speed does matter on standardized tests.</p>