The steepness of a line expressed as rise over run, connecting the algebraic slope formula to the geometric angle of inclination.
A ramp's steepness—the ratio of how high it rises to how far it goes horizontally.
Showing a random 20 of 50 problems.
Example 1
easy
A slope of 1 corresponds to what angle with the horizontal?
Example 2
easy
Why is the slope of a vertical line undefined?
Example 3
challenge
Explain why slope is the same between ANY two points on a given line, and why this fails for a curve.
Example 4
challenge
A line through (2,3) with negative slope m cuts off a triangle from the first quadrant with the coordinate axes. Find the slope m that minimizes the length of the segment between the two axis intercepts.
Example 5
challenge
A line through the origin has inclination angle θ such that the line passes through (4,3). Find tanθ and sinθ.Line through the origin and (4, 3) with its 3-4-5 right triangle
Example 6
easy
A line goes down from left to right. Is its slope positive or negative?
Example 7
easy
What is the slope of a horizontal line?
Example 8
easy
Which of these lines is steeper: y=5x+2 or y=−7x−3? Which has a greater angle with the x-axis?
Example 9
easy
A wheelchair ramp rises 0.5 m over a run of 6 m. What is its slope?
Example 10
medium
A line has slope −43. If it rises (changes y) by −6, what is the change in x?
Example 11
medium
Find the slope of the line that is perpendicular to 2x−5y=10.
Example 12
hard
Slope of the line through (a,a2) and (b,b2) on the parabola y=x2 equals ___ (in terms of a and b).
Example 13
easy
Find the slope of the line through (−5,2) and (3,−2).Find the slope of the line through (−5, 2) and (3, −2)
Example 14
hard
A treadmill is inclined at 7.5% grade. What is the angle of incline to the nearest tenth of a degree?
Example 15
medium
The median rent in a city rose from $1,200 in 2018 to $1,560 in 2022. Treating year as x and rent as y, find the slope (units $/year).
Example 16
medium
Points A(1,2), B(4,k), C(7,14) are collinear. Find k.Three collinear points; find the missing y-coordinate k at x
Example 17
easy
If a line passes through (0,4) and (5,4), its slope is ___.Line through (0, 4) and (5, 4) — what is the slope?
Example 18
hard
Find the slope of the line tangent to the circle x2+y2=25 at the point (3,4).
Example 19
medium
Why does a constant slope mean the line is straight?