➕ Algebra 1 · Linear Functions
Point-Slope Form flashcards
Say the answer out loud before you flip. Cards you miss come back sooner; cards you know come back later. That spacing is what builds long-term memory.
All 14 flashcards at a glance
Card 1
What does each letter mean in y − y1 = m(x − x1)?
m is the slope. (x1, y1) is one known point on the line. x and y stay as letters: they stand for any point on the line.
Card 2
Read the slope and a point from y + 5 = 4(x + 1).
m = 4. The y + 5 is y − (−5) and the x + 1 is x − (−1), so the point is (−1, −5).
Card 3
Rewrite x + 12 as a subtraction. What is x1?
x + 12 = x − (−12), so x1 = −12.
Card 4
Write the equation of the line with slope −5 through (3, 4).
y − 4 = −5(x − 3)
Card 5
Write the equation of the line with slope 1/3 through (−9, −6).
y − (−6) = (1/3)(x − (−9)), which simplifies to y + 6 = (1/3)(x + 9).
Card 6
A line passes through (1, 5) and (3, 11). What do you do first?
Find the slope: (11 − 5) ÷ (3 − 1) = 3. Then use either point: y − 5 = 3(x − 1).
Card 7
In this lesson’s “flip the sign” trick, what do you do with the sign next to x or y in y − y1 = m(x − x1)?
Flip it to get the point’s coordinate. x + 20 gives x1 = −20, and y − 16 gives y1 = 16.
Card 8
Convert y − 4 = 3(x − 2) to slope-intercept form.
Distribute: y − 4 = 3x − 6. Add 4 to both sides: y = 3x − 2.
Card 9
Why can’t a vertical line be written in point-slope form?
Its slope is undefined (the run is 0), so there is no number to use for m. Write it as x = a instead.
Card 10
Does a non-vertical line have only one point-slope equation?
No. Any point on the line can be the known point. For example, y − 1 = 2x and y − 5 = 2(x − 2) both simplify to y = 2x + 1.
Card 11
What is the point-slope equation of the horizontal line through (−3, 4)?
The slope is 0, so y − 4 = 0(x + 3), which simplifies to y = 4.
Card 12
A phone battery is at 60 percent after 2 hours and drains 15 percentage points per hour. Write an equation for the battery level B after t hours.
B − 60 = −15(t − 2). The slope is −15 because the level falls. It simplifies to B = −15t + 90, so the battery started at 90 percent. It only fits until the battery reaches 0 percent, at t = 6.
Card 13
In a story, what does m(x − x1) tell you?
x − x1 is how far x has moved from the known point. Multiplying by the rate m gives how much y has changed since that point.
Card 14
In terms of the known point and the slope, what is b?
b = y1 − m × x1. It comes from distributing the slope and moving y1 to the right side.