In the -plane, the line represented by
is graphed. What is the slope of the line?
A line’s slope tells how much changes for each -unit increase in , but parentheses and a coefficient on can hide it. Graph the given equation in Desmos to check whether the line rises or falls, then get alone and read the number multiplying . A minus sign in the original equation does not, by itself, tell you the slope’s sign.
Hints
- Hint 1
A slope is positive if the line rises as you move right and negative if it falls. Graph the equation as written in Desmos. Which direction does the line go?
- Hint 2
To read slope from an equation, write it in slope-intercept form, , where is the slope. First distribute to both terms inside the parentheses.
- Hint 3
The multiplies , so getting alone means dividing every term on both sides by . What number will then multiply ?
Step-by-step
Check the sign, then isolate
Step 1Check which way the line goes
A slope measures the change in as increases. Type in Desmos. The line rises as you move right, so its slope must be positive. The in the equation does not settle the slope’s sign.
- Step 2
Distribute the negative number
Multiply by both terms in the parentheses. In particular, times is positive:
- Step 3
Remove the constant on the left
Subtract from both sides:
- Step 4
Move the term
Add to both sides so only the term remains on the left:
- Step 5
Get alone and read the slope
Divide every term by :
In slope-intercept form , the slope is , the number multiplying . Get alone before reading that coefficient. Here the line’s slope is , so it rises unit for each unit to the right. Choice D.