Question 62·Medium·Linear Equations in Two Variables
In the -plane, what is the -intercept of the line that passes through and is parallel to the line ?
For SAT questions about lines parallel to a given line, first convert the given equation to slope-intercept form to read off the slope quickly. Use that same slope for the new line, plug in the given point to solve for (the -intercept), and then match that value to the answer choices. Keep the idea clear: parallel means same slope, not same intercept.
Hints
Rewrite the given line
Start by putting into the form so you can easily see its slope.
Use the idea of parallel lines
What stays the same for lines that are parallel: their slopes or their intercepts?
Write the new line's equation
Once you know the slope, write the equation of the new line as , then plug in the point to find .
Interpret
Remember that in the equation , the -intercept is the value of when , which is the constant .
Desmos Guide
Graph the original line and find its slope
Type 4x - 2y = 10 into Desmos. Click on the graph or rewrite it visually as y = 2x - 5 to see that the slope is .
Write and graph the parallel line through (2, -3)
In Desmos, enter y = 2x + b (using a slider for b). Then add the point (2, -3) and adjust the slider until the line passes through that point. Note the value of b when the line goes exactly through (2, -3); that value is the -intercept.
Step-by-step Explanation
Find the slope of the given line
Rewrite in slope-intercept form .
So the slope of this line is .
Use the fact that parallel lines have the same slope
A line parallel to must also have slope . So the equation of the new line has the form
for some -intercept that we need to find.
Plug in the point the new line passes through
The new line passes through , so its coordinates must satisfy .
Substitute and :
Now solve for .
Solve for the y-intercept
From , subtract from both sides:
So the -intercept is , which corresponds to choice D.