Two points determine a line's slope, the change in for each increase in . Plot the points in Desmos to see whether the line rises or falls, then divide the change in by the change in . Use one point to find where the line crosses the -axis. A point with is not necessarily the -intercept.
Hints
- Hint 1
The slope tells you how changes as increases. Plot the two points and look from left to right: does the line rise or fall? That tells you whether its slope is positive or negative.
- Hint 2
To calculate slope, put the change in above the change in . Subtract the coordinates in the same point order on top and bottom. What fraction do the two given points make?
- Hint 3
In slope-intercept form , is the value of when . Use the slope and one given point to find it. A point where doesn't give you unless is also .
Step-by-step
Find the slope, then the intercept
Step 1Check which way the line runs
Type and in Desmos. From the first dot to the second, you move right and up, so the line has a positive slope: increases as increases.
- Step 2
Find the slope
Divide the change in by the change in , subtracting in the same order on top and bottom. Type in Desmos. It shows , or using the fraction button. That's the line's slope.
- Step 3
Find the intercept and write the line
In , is the -intercept, the value of when . The point says when , so put that point and the slope into the equation: . Type ; the asks Desmos to find . Under PARAMETERS, it shows . The line through both points is . Choice C.