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The symbol for Slope Formulais. is the rate of change of the
dependent variable “y” with respect to the independent variable“x”. To find the of a line pick two points from the line:
Put these points into the formula for(^ ,^ ) and^ (^. ,^ It does not matter ).
which points you pick for which formula you use. the values from the What does matter is that you subtract andvalues or that you subtract nor does it matter
the the formula. values from the values as shown below in
Example, find the slope of the line with points ( , ) and (both formulas to verify you get the same slope. , ). Use
slope^ slope^ m^ Slope
point 1 x 1 y 1 point 1 slope
point 1 point 1
point 2 x 2 y 2
point 2^ point 2
point 2
m (^) = yx^22 - y - x^11 = -7^8 - -^32 = -9^5 = - 95 m =^ yx^11 - y - x^22 = 32 - -^8 -7 = -5 9 = -^59
m (^) =^ change in ychange in x = riserun = yx^22 - y - x^11 = yx^11 - y - x^22
Slope-Intercept Form of an Equation Y-intercept b y-intercept b
intersects, intercepts, comes in contact with,meets, shares a common point, engages with the^ , the point where the line crosses, y-axis. The number by itself including the sign infront of it is. It is an actual point with an x-coordinate and a y-coordinate. This formula only uses the value ofthe y-coordinate which is what “ ” stands for. Thewhen you start the graph of the equation. is the first point you plot Themultiplied by. If it is not a fraction put a 1 under itto make it a fraction. is. This is the number that x is The tells you how to get to the next point. you how many spaces to move vertically and thesign tells which direction, up if positive down if The number on top tells negative. The bottom number tells you how manyspaces to move horizontally and the sign tells thedirection, left if negative right if positive.
slope m slope
y = mx + b
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m = -2b = 4Write the equation in slope-intercept formand graph it. m = 2b = -4Write the equation in slope-intercept formand graph it.
m = -2b = -4Write the equation in slope-intercept formand graph it.. m = 2b = 4Write the equation in slope-intercept formand graph it.
Equation to Find the Slope and Y-InterceptUsing the Slope-Intercept Form of an Only when an equation is in slope-intercept formwill you be able to just look at it and know whatthe is and the is. The slopey-interceptsign in front of it). is the number x is multiplied by and the is the number by itself (including the For example in the equation y =is and the y-intercept is. x the slope When an equation is not solved for y it is notin slope-intercept form so this does not work.You need to put it in slope-intercept form by solving for y first before you can apply thistrick. For example y + 6x = 12 is not in slope-interceptform. The slope is not 6. Solving for y you gety = -6x +12. Now it is in slope-intercept form so the slope m is -6 and the y-intercept b is 12.
slope mm 3 3 m
b^ y-intercept b b -9^ -
y = mx + b
Put inequalities in slope-intercept form by solvingGraphing Inequalities
for y before graphing them. Make sure that y ison the left side of the equation. Once that is donethe inequality tells you everything you need to make the graph.All the graphs start at the y- intercept. The slope The inequality operator tells you if you need asolid line or a dashed line, tells you how to get to the next point solid line if the. inequality operator has a solid line under it,dashed line if no line under the inequalityoperator. The inequality operator also tells you which side to shade. shade above if > or (^) Shade below if ³. < or £ ,
m b
yy xx solid line, shade belowsolid line, shade above yy <>xx dashed line, shade belowdashed line, shade above
mm mm
m =b =Shade up or down?Solid or dashed line?Write the inequality in slope-intercept form. m =b =Shade up or down?Solid or dashed line?Write the inequality in slope-intercept form.
m =b =Shade up or down?Solid or dashed line?Write the inequality in slope-intercept form. m =b =Shade up or down?Solid or dashed line?Write the inequality in slope-intercept form.
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Point-Slope Form of an Equation The point (theThe minus sign in front of of the line. “y” and “x” are the variables y and x. , ) is any point on the line. The value of is not part of and the minus is sign in front ofof the formula and must be there for it to work correctly. Forexample if you are given the equation y + 7 = 3(x + 9) you is not part of. The minus signs are part need to replace the + with a - - so that the equation is in thecorrect form. The correct form is y - -7 = 3(x - -9).you can correctly pick out the value for which is -7 and Now There are two situations when this form is useful:which is -9. You are given one point and the slope.You are given two points. If you know one point and the slope just put them in and youhave the equation. Since you know a point and the slopeyou can graph the equation. Start at the point and use the slope to get to the next point.If you know two points you will have to calculate the slope using the slope formula. Once you know the slope you canplug it in along with either point and you have the equation.Although the equations will look different for each point they will look the same when you solve them for y. Graphing theequation when you know two points is easiest of all. Justplot both points and draw the line through them.
x 1 y (^1) y 1 y 1 x 1 x 1
x 1 y^1
slope^ y -^ y^1 =^ m(x -^ x^1 )^ m
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m = -2, the point is (3,4).Write the equation in point-slope form andgraph it. Now solve it for y so you canfigure out the y-intercept. m = 2, the point is (-3,-4).Write the equation in point-slope form andgraph it. Now solve it for y so you canfigure out the y-intercept.
The two points are (5,6) and (-1,-2)Write the equation in point-slope form andgraph it. Now solve it for y so you canfigure out the y-intercept. The two points are (2,3) and (4,7)Write the equation in point-slope form andgraph it. Now solve it for y so you canfigure out the y-intercept.
Standard Form of an Equation A, B and C are integers not decimals or fractions and A andB can not be zero at the same time. This is best used to findthe x-intercept and the y-intercept of the equation. Y-intercept intersects, intercepts, comes in contact with,meets, shares a common point, engages with the, the point where the line crosses, y-axis. This is a point with an x-coordinate that isalways zero but a y-coordinate that is the valueon the y-axis where the line crosses the y-axis. If you solved the equation for y the value of the y-intercept would be “b”. X-intercept intersects, intercepts, comes in contact with,meets, shares a common point, engages with the, the point where the line crosses, x always zero but an x-coordinate that is the valueon the x-axis where the line touches the x-axis.-axis. This is a point with a y-coordinate that is
Ax + By = C
Standard Form of an Equation,Finding the x and the y-intercepts
Since thecrosses the y-axis. The x-coordinate of that point isalways zero Put a zero in for x and you get a simpler y-intercept is the point where the line equation By = C. Just solve for y and you have the y-intercept. Find the y-intercept of:5(0) + 10y = 205x + 10y = 20 10y = 20y= Since thecrosses the x-axis. The y-coordinate of that point isalways zero Put a zero in for y and you get a simpler x-intercept is the point where the line equation Ax = C. Just solve for x and you have the x-intercept. Find the x-intercept of:5x + 10(0) = 205x + 10y = 20 5x = 20x=
Ax + By = C
Graphing Horizontal and Vertical Lines x = a (vertical line), y = c (horizontal line)
Equations of the form x = a have no y in them so they never crossthe y-axis, they might be on the y-axis but they do not cross it.Every point that has a value of
x = a is on the line so you get a line that goes straight up anddown. Equations of the form y = c have no x in them so they nevercross the x-axis, they might be on the x-axis but they do not cross
it. Every point that has a value of y = c is on the line so you get aline that goes horizontally left to right.
To graph the equation x = 5, pick two points that have x = 5 andtwo different y values. Try (5,2) and (5, -4), plot these points belowand draw a line through them. Try the same thing for y = 2. Pick
two points with y = 2 and two different x values. Try (1,2) and (7,2). Plot these and draw a line through them.
-3-2-1^1
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