Card 1 of 20
EasyStudy card 1
Prompt
State slope-intercept form.
Read coefficient and constant.
Answer
\(y=mx+b\), where m is slope and b is the y-intercept.
Example
\(y=3x-2\) has slope 3 and y-intercept \((0,-2)\).
MathChapter 3: Functions and Linear Equations
Flashcards
Slope-Intercept Form and Point-Slope Form Flashcards
Twenty original recall cards covering 3-3 slope-intercept form and point-slope form concepts, procedures, graphs, and traps.
Current card1 / 20
Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
State point-slope form.
It uses one point and slope.
Answer
\(y-y_1=m(x-x_1)\).
Example
Through \((2,5)\) with slope 3: \(y-5=3(x-2)\).
Card 3 of 20
EasyStudy card 3
Prompt
What does b represent in y = mx + b?
It is not the x-intercept.
Answer
The y-coordinate of the y-intercept \((0,b)\).
Example
If \(b=-4\), the line crosses at \((0,-4)\).
Card 4 of 20
MediumStudy card 4
Prompt
When is point-slope form especially useful?
No intercept is required.
Answer
When a point and the slope are known.
Example
Use either known point from a two-point problem.
Card 5 of 20
MediumStudy card 5
Prompt
How does point (-3,4) appear in point-slope form?
Subtracting negative 3 becomes plus 3.
Answer
As \(y-4=m(x+3)\).
Example
Keep the template visible to avoid sign errors.
Card 6 of 20
MediumStudy card 6
Prompt
How do you write a line from two points?
Verify the unused point.
Answer
Find slope, substitute either point into point-slope form, then convert if needed.
Example
Two distinct x-values define one nonvertical line.
Card 7 of 20
MediumStudy card 7
Prompt
How do you convert point-slope to slope-intercept form?
Preserve equality.
Answer
Distribute, then isolate y and combine constants.
Example
\(y-1=2(x-3)\) becomes \(y=2x-5\).
Card 8 of 20
MediumStudy card 8
Prompt
How do you convert slope-intercept to standard form?
Use integer coefficients when requested.
Answer
Move x and y terms to one side and clear fractions if needed.
Example
\(y=2x+3\) becomes \(2x-y=-3\).
Card 9 of 20
MediumStudy card 9
Prompt
How do you find b from a slope and point?
Substitute the point coordinates.
Answer
Use \(b=y-mx\).
Example
Slope 2 through \((3,8)\) gives \(b=2\).
Card 10 of 20
MediumStudy card 10
Prompt
How do you read a line equation from a graph accurately?
Do not estimate from line thickness.
Answer
Use two exact labeled points for slope, then read or calculate the intercept.
Example
Lattice points reduce error.
Card 11 of 20
MediumStudy card 11
Prompt
What sign error occurs with a negative x-coordinate?
Point-slope uses subtraction.
Answer
Writing \(x-3\) instead of \(x-(-3)=x+3\).
Example
The visible sign reverses for a negative coordinate.
Card 12 of 20
MediumStudy card 12
Prompt
What sign error occurs with a negative y-coordinate?
Use y minus y1.
Answer
Writing \(y-4\) instead of \(y-(-4)=y+4\).
Example
Through \((2,-4)\): \(y+4=m(x-2)\).
Card 13 of 20
MediumStudy card 13
Prompt
How do you find the x-intercept from y = mx + b?
b is not generally the x-intercept.
Answer
Set y equal to zero and solve \(0=mx+b\).
Example
The x-intercept is \(-b/m\) when \(m\ne0\).
Card 14 of 20
MediumStudy card 14
Prompt
Can equivalent line equations look different?
Compare after simplifying.
Answer
Yes. Multiplying every term by the same nonzero constant preserves the line.
Example
\(y=2x+1\) and \(2x-y=-1\) match.
Card 15 of 20
MediumStudy card 15
Prompt
What check confirms a written line equation?
Use unused data.
Answer
Substitute each known point and confirm both sides agree.
Example
A graph's intercept is another quick check.
Card 16 of 20
MediumStudy card 16
Prompt
What is the point-slope equation through (0,b)?
The forms are connected.
Answer
\(y-b=m(x-0)\), which simplifies to \(y=mx+b\).
Example
The y-intercept itself can be the chosen point.
Card 17 of 20
MediumStudy card 17
Prompt
Why clear fractions in standard form?
Multiply every term.
Answer
It produces conventional integer coefficients without changing the line.
Example
Multiply \(y=(3/2)x-1\) by 2 before rearranging.
Card 18 of 20
MediumStudy card 18
Prompt
What information determines a unique nonvertical line?
A slope alone gives a family of parallel lines.
Answer
Two distinct points, or one point plus a slope.
Example
An intercept fixes one member of that family.
Card 19 of 20
MediumStudy card 19
Prompt
What does changing b do while m stays fixed?
Slope remains unchanged.
Answer
It shifts the line vertically to a parallel line.
Example
\(y=2x+1\) and \(y=2x-4\) are parallel.
Card 20 of 20
MediumStudy card 20
Prompt
What does changing m do while b stays fixed?
The lines pivot through \((0,b)\).
Answer
It changes steepness/direction while keeping the same y-intercept.
Example
Different slopes intersect once.
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