Question

Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *​

Answer 1

Here are a couple I found:

Similarities:

• They have the same y-intercept of (0,5).
• They are both in slope-intercept form.

Differences:

• The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
• They have different x-intercepts. (y = 2x + 5 intersects (-$\frac{5}{2}$, 0) while y = -13x + 5 intersects at ($\frac{5}{13}$, 0)

Explanation:

Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).

As for differences, we can see that the coefficient in place of that "m" is positive in y = 2x + 5 and negative in y = -13x + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.