The lines have the same y-intercept, but one line has a steep positive slope and the other has a less steep negative slope.
Practice makes perfect
Notice that both equations are given in a slope-intercept form, which follows a specific format.
y=mx+ b
In this form, m represents the slope of the line and b represents the y-intercept. Now we can graph the given lines!
y=2x+5
Let's identify the key features of this equation.
Equation
Slope
y-intercept
y=2x+ 5
2
5
To graph the equation, we can plot the y-intercept and then use the slope to find another point on the line. A slope of 2 means that for every 1 unit we move to the right, we move 2 units up.
y=-1/3x+5
Now we will graph the second equation on the same coordinate plane to compare them! Again, we can begin with identifying the key features of the equation.
Equation
Slope
y-intercept
y=- 13x+ 5
- 13
5
To graph the equation, we can plot the y-intercept and then use the slope to find another point on the line. A slope of - 13 means that for every 3 units we move to the right, we move 1 unit down.
Comparison
Finally, let's compare the lines! We can tell that both have the same y-intercept. However, notice that line y=2x+5 is steeper and has a positive slope. The line y=- 13 x+5 is less steep and has a negative slope.
