To find the slope of a line passing through two points, use the formula m = (y₂ - y₁)/(x₂ - x₁), where (x₁,y₁) and (x₂,y₂) are the coordinates of the two points
How do I find the slope of the line?
Pick any two points on the line, subtract their y-coordinates for the rise, subtract their x-coordinates for the run, then divide rise by run
Label your points (x₁,y₁) and (x₂,y₂). Calculate rise = y₂ − y₁ and run = x₂ − x₁. Finally, compute slope m = rise/run. For example, if your points are (1,2) and (4,8), rise = 8 − 2 = 6 and run = 4 − 1 = 3, so m = 6/3 = 2. The result tells you how many units the line climbs for every one unit it moves right.
What is the slope of the line that passes through the points (-2, 5) and (-3, 6)?
Plug the points into m = (y₂ − y₁)/(x₂ − x₁). Using (–3,6) as (x₂,y₂) gives m = (6 − 5)/(–3 − (–2)) = 1/(–1) = –1. A negative slope means the line tilts downward as you move from left to right, like a downhill ski trail.
Which is the slope of the line that passes through the points (3, 17) and (7, 25)?
Compute m = (25 − 17)/(7 − 3) = 8/4 = 2. A slope of 2 says the line rises two units vertically for every one unit it goes horizontally; think of a staircase that climbs two steps for each step forward.
How do you find slope given two points?
Use the slope formula m = (y₂ – y₁)/(x₂ – x₁) with the coordinates of the two points
Identify the first point as (x₁,y₁) and the second as (x₂,y₂). Calculate the differences, then divide. If you reverse the points, the sign of the result flips, but the absolute value stays the same. This method works for any pair of points in a plane, even if one coordinate is negative or zero.
What is the slope of the line 2y = 3x + 4?
Rewrite the equation as y = (3/2)x + 2 to put it in slope-intercept form y = mx + b. The coefficient of x is the slope, so m = 3/2. That means for every two units you move horizontally, the line rises three units vertically, like a gentle ramp.
What is a positive slope?
A positive slope means the line tilts upward as you move from left to right, showing that y increases when x increases
Graphically, the line climbs as you scan from left to right. A slope of 0.5 indicates a gentle incline; a slope of 5 indicates a steep incline. In real life, a positive slope could represent the rate at which your savings grow over time or how far a car travels as the engine runs longer.
What is the slope of the line y = 3?
In y = 3, the coefficient of x is zero, so m = 0. The line is perfectly horizontal, never rising or falling no matter how far you travel left or right. Think of a calm lake surface—no matter which direction you look, the height doesn’t change.
What is the slope of the line that passes through the points (-2, 5) and (1, 4)?
Apply the slope formula: m = (4 − 5)/(1 − (–2)) = –1/3. A negative slope means the line falls as you move right; in this case, it drops one unit for every three units it advances, like a mild downhill path.
What is the slope of the line 2y = 3x + 6?
Solving for y gives y = (3/2)x + 3, so the slope is the coefficient of x, which is 3/2. This tells you the line rises 1.5 units for every 1 unit it moves right, a moderately steep incline.
What is the slope of 2x – 4y = 8?
Rearrange to slope-intercept form: –4y = –2x + 8, then y = (1/2)x – 2. The slope is the coefficient of x, so m = 1/2. Picture a ramp that rises one unit for every two units forward.
What is an equation of the line with a slope of 1/4 and a y-intercept of –3?
The equation is y = (1/4)x – 3
Using y = mx + b, plug in m = 1/4 and b = –3 to get y = (1/4)x – 3. This line crosses the y-axis at –3 and slopes upward gently, rising one unit for every four units it moves right.
What are 4 types of slopes?
The four types are positive, negative, zero, and undefined (infinite)
- Positive slope: line rises left to right
- Negative slope: line falls left to right
- Zero slope: flat horizontal line
- Undefined slope: perfectly vertical line
Think of a mountain’s side (positive), a downhill trail (negative), a flat valley floor (zero), and a cliff face (undefined) to keep them straight.
What is a zero slope look like?
A zero slope looks like a perfectly flat horizontal line with equation y = constant
The line never tilts up or down; it’s parallel to the x-axis. For example, y = 5 is a horizontal line that stays at height 5 no matter what x is, like the surface of a calm swimming pool.
How do you know when a slope is positive?
A slope is positive when the line tilts upward from left to right, meaning the y-value increases as the x-value increases
Visually, imagine walking uphill as you go right. Numerically, the slope m > 0. In data terms, if study hours (x) increase and test scores (y) rise, the relationship has a positive slope.
What is the run of Y = 3?
The run can be any real number because the line is horizontal, but the rise is always zero
For y = 3, the rise = 0 and run = any Δx. Therefore, slope = 0/Δx = 0, confirming the flat line. In practical terms, if you walk along the line, you move left or right (run) but never up or down (rise).
What is the slope of the line that passes through the points (-2, 5) and (-3, 6)?
Plug the points into m = (y₂ − y₁)/(x₂ − x₁). Using (–3,6) as (x₂,y₂) gives m = (6 − 5)/(–3 − (–2)) = 1/(–1) = –1. A negative slope means the line tilts downward as you move from left to right, like a downhill ski trail.
Which is the slope of the line that passes through the points (3, 17) and (7, 25)?
Compute m = (25 − 17)/(7 − 3) = 8/4 = 2. A slope of 2 says the line rises two units vertically for every one unit it goes horizontally; think of a staircase that climbs two steps for each step forward.
What is the slope of the line 2y = 3x + 4?
Rewrite the equation as y = (3/2)x + 2 to put it in slope-intercept form y = mx + b. The coefficient of x is the slope, so m = 3/2. That means for every two units you move horizontally, the line rises three units vertically, like a gentle ramp.
What is the slope of the line y = 3?
In y = 3, the coefficient of x is zero, so m = 0. The line is perfectly horizontal, never rising or falling no matter how far you travel left or right. Think of a calm lake surface—no matter which direction you look, the height doesn’t change.
What is the slope of the line that passes through the points (-2, 5) and (1, 4)?
Apply the slope formula: m = (4 − 5)/(1 − (–2)) = –1/3. A negative slope means the line falls as you move right; in this case, it drops one unit for every three units it advances, like a mild downhill path.
What is the slope of the line 2y = 3x + 6?
Solving for y gives y = (3/2)x + 3, so the slope is the coefficient of x, which is 3/2. This tells you the line rises 1.5 units for every 1 unit it moves right, a moderately steep incline.
What is the slope of 2x – 4y = 8?
Rearrange to slope-intercept form: –4y = –2x + 8, then y = (1/2)x – 2. The slope is the coefficient of x, so m = 1/2. Picture a ramp that rises one unit for every two units forward.
What is an equation of the line with a slope of 1/4 and a y-intercept of –3?
The equation is y = (1/4)x – 3
Using y = mx + b, plug in m = 1/4 and b = –3 to get y = (1/4)x – 3. This line crosses the y-axis at –3 and slopes upward gently, rising one unit for every four units it moves right.
What are 4 types of slopes?
The four types are positive, negative, zero, and undefined (infinite)
- Positive slope: line rises left to right
- Negative slope: line falls left to right
- Zero slope: flat horizontal line
- Undefined slope: perfectly vertical line
Think of a mountain’s side (positive), a downhill trail (negative), a flat valley floor (zero), and a cliff face (undefined) to keep them straight.
What is a zero slope look like?
A zero slope looks like a perfectly flat horizontal line with equation y = constant
The line never tilts up or down; it’s parallel to the x-axis. For example, y = 5 is a horizontal line that stays at height 5 no matter what x is, like the surface of a calm swimming pool.
How do you know when a slope is positive?
A slope is positive when the line tilts upward from left to right, meaning the y-value increases as the x-value increases
Visually, imagine walking uphill as you go right. Numerically, the slope m > 0. In data terms, if study hours (x) increase and test scores (y) rise, the relationship has a positive slope.
What is the run of Y = 3?
The run can be any real number because the line is horizontal, but the rise is always zero
For y = 3, the rise = 0 and run = any Δx. Therefore, slope = 0/Δx = 0, confirming the flat line. In practical terms, if you walk along the line, you move left or right (run) but never up or down (rise).
