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Math · 23 · Algebra

Linear Graphs I

Notes

Key points

  • Slope = rise over run. m>0m>0 rises, m<0m<0 falls.
  • Slope-intercept y=mx+by=mx+b: bb is the y-intercept.
  • Point-slope y−y1=m(x−x1)y-y_1=m(x-x_1): use when given a point and a slope.
  • Standard form Ax+By=CAx+By=C: slope −AB-\tfrac{A}{B}, no rearranging needed.
  • Word problems: slope = rate per unit; y-intercept = starting value.
  • Horizontal line: m=0m=0. Vertical line: slope undefined.

Formulas

Slopem=y2−y1x2−x1m=\dfrac{y_2-y_1}{x_2-x_1}Not on the reference sheet
Slope-intercept formy=mx+by=mx+b
Point-slope formy−y1=m(x−x1)y-y_1=m(x-x_1)
Standard formAx+By=Cm=−AB,  y-int=CBAx+By=C\qquad m=-\dfrac{A}{B},\ \ y\text{-int}=\dfrac{C}{B}
x-intercept of y = mx + bx=−bmx=-\dfrac{b}{m}

Common traps

  • Mismatched order: y2−y1x1−x2\tfrac{y_2-y_1}{x_1-x_2} flips the sign. Keep the points in step.
  • Reading the slope of 2y=6x+42y=6x+4 as 6. Divide by 2 first: m=3m=3.
  • Counting gridlines for rise and run without checking the axis scales.

SAT tip

Interpretation questions: slope = change in y for each 1 unit of x, in the problem's units. Say it aloud first.

Test yourself

10 official SAT questions on Linear Graphs I, easiest first.

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