- WELCOME TO A VIDEO THAT WILL SHOW YOU HOW TO GRAPH LINES
ON THE TI-83 OR TI-84 GRAPHING CALCULATOR
USING THE GRAPHING FEATURE AS WELL AS THE TABLE FEATURE.
SO LET'S SAY WE WANT TO GRAPH THE LINE Y = -2X + 3.
SLOPE INTERCEPT FORM IS THE PERFECT FORM
TO ENTER INTO THE GRAPHING CALCULATOR
BECAUSE THE GRAPHING CALCULATOR DOES REQUIRE THE EQUATION
TO BE SOLVED FOR Y.
SO IF WE HAVE OUR CALCULATOR,
THE FIRST THING WE'LL DO IS PRESS Y EQUALS
AS WE SEE HERE ON THE TOP LEFT.
IF YOU HAVE ANY OTHER EQUATIONS IN Y1, Y2,
AND SO ON, WE DO WANT TO CLEAR THOSE,
AND WE CAN DO THAT BY JUST PRESSING CLEAR
AND THEN ARROW DOWN, CLEAR, ARROW DOWN, AND CLEAR.
NOW WE'LL GO BACK UP TO Y1 AND ENTER THE EQUATION.
NOTICE THAT THE Y EQUALS IS ALREADY THERE,
SO WE JUST NEED TO TYPE IN -2X + 3.
BE CAREFUL. WE CAN'T TYPE IN - 2X.
IT HAS TO BE -2X,
SO WE'LL USE THE NEGATIVE SIGN BELOW THE 3, 2.
THIS KEY HERE IS FOR THE VARIABLE X AND THEN + 3.
NOW BEFORE WE PRESS GRAPH,
LET'S MAKE SURE WE HAVE THE STANDARD WINDOW
WHICH MEANS BOTH AXES WILL GO FROM -10 TO 10.
A QUICK EASY WAY TO MAKE SURE WE HAVE THE STANDARD VIEWING WINDOW
IS TO PRESS ZOOM AND THEN OPTION 6 OR Z STANDARD.
AND NOW YOU SHOULD SEE THE LINE GRAPHED ON THE SCREEN.
IF WE DO PRESS THE WINDOW KEY,
YOU'LL NOTICE BOTH THE X MINIMUM AND Y MINIMUM ARE -10,
AND THE X MAX AND Y MAX ARE ALSO 10.
NOW LET'S GO AHEAD AND PRESS GRAPH AGAIN,
AND THIS GIVES US A NICE VISUAL
OF WHAT THE LINE SHOULD LOOK LIKE,
BUT IT DOESN'T GIVE US EXACT POINTS
TO PLOT ON OUR COORDINATE PLANE TO MAKE A NICE GRAPH
OF THE LINE.
IF WE PRESS TRACE THIS DOES GIVE US THE POINT (0, 3),
BUT IF WE PRESS THE RIGHT OR LEFT ARROW,
NOTICE THESE OTHER POINTS ON THE LINE
DON'T COME OUT TO NICE X AND Y VALUES.
AND THIS IS WHERE THE TABLE FEATURE COMES IN VERY HANDY.
THE TABLE FEATURE WOULD SHOW WHAT YOU WOULD HAVE
IF YOU MADE A T-TABLE FOR THIS LINE.
SO LET'S PRESS 2nd WINDOW TO SET UP THE TABLE FEATURE.
WE'RE GOING TO START THE TABLE AT 0.
THE CHAIN IN THE TABLE WILL BE BY 1s.
THAT'S GOOD.
WE WANT TO MAKE SURE THAT THE INDEPENDENT VARIABLE HERE
IS ON AUTOMATIC,
SO WE'RE GOING TO HIGHLIGHT AUTOMATIC AND THEN PRESS ENTER.
NOW WE'RE READY TO GO TO THE TABLE.
NOTICE THAT RIGHT ABOVE THE GRAPH BUTTON
THERE'S TABLE WRITTEN IN BLUE,
SO TO ACCESS A TABLE WE HAVE TO PRESS 2nd GRAPH.
AND NOW WE CAN SCROLL UP AND DOWN THIS T-TABLE
TO FIND THE COORDINATES OF AN INFINITE NUMBER OF POINTS
THAT WOULD BE ON THIS LINE.
SO HERE'S THE 0.03, THEN THERE'S THE 0.11, 2, -1, AND SO ON.
WE ONLY NEED TWO OF THESE POINTS
TO MAKE A NICE, ACCURATE GRAPH OF THIS LINE,
SO LET'S GO AHEAD AND PLOT (0, 3) AND (3, -3).
SO HERE'S THE POINT (0, 3), AND HERE'S THE POINT (3, -3).
SO OUR LINE PASSES THROUGH THOSE TWO POINTS.
NOW THIS PROBABLY WAS A LOT OF WORK TO GRAPH THIS LINE
BECAUSE IT IS IN SLOPED INTERCEPT FORM,
MEANING THE Y-INTERCEPT IS 3 AS WE SEE HERE.
THE SLOPE IS -2 OR -2/1, SO FROM HERE WE'D GO DOWN 2 AND RIGHT 1.
AND OF COURSE, WE'D HAVE THE SAME LINE.
LET'S GO AHEAD AND TRY ANOTHER ONE.
HERE WE HAVE Y = 2/3X - 5.
WE DO HAVE TO BE A LITTLE CAREFUL
WHEN WE HAVE A FRACTIONAL SLOPE IN SLOPED INTERCEPT FORM,
SO LET'S GO BACK TO THE GRAPHING CALCULATOR.
PRESS Y EQUALS.
CLEAR OUT THIS LINE.
WE'RE GOING TO ENTER IN (2/3) IN A SET OF PARENTHESES,
SO WE'LL HAVE AN OPEN PARENTHESIS
2 DIVIDED BY 3 CLOSED PARENTHESIS.
PRESS X - 5.
NOW WE CAN GRAPH THE LINE.
PRESS GRAPH.
THERE'S THE LINE.
IF WE WANT TO FIND SPECIFIC POINTS ON THIS LINE,
WE CAN NOW JUST PRESS 2nd GRAPH TO ACCESS THE TABLE.
NOTICE SEVERAL OF THE Y COORDINATES
ARE REPEATING DECIMALS.
REMEMBER WHEN WE GRAPHED THESE BY MAKING T-TABLES,
AND WE HAD A FRACTIONAL SLOPE,
WE ALWAYS CHOSE X VALUES
THAT WERE MULTIPLES OF THE DENOMINATOR,
SO IF WE LOOK AT MULTIPLES OF 3 IN THE TABLE,
THESE WILL BE THE VALUES WHERE Y IS AN INTEGER
RATHER THAN A REPEATING DECIMAL.
SO LET'S USE THE POINTS (0, -5) AND (3, -3).
HERE'S (0, -5) AND (3, -3) WOULD BE HERE.
OUR LINE PASSES THROUGH THESE TWO POINTS,
AND AGAIN JUST TO VERIFY WE HAVE A Y-INTERCEPT OF -5.
OUR SLOPE IS 2/3, SO IF WE GO UP 2, RIGHT 3,
THERE'S OUR SECOND POINT.
THEN JUST TO VERIFY,
IF WE PRESS GRAPH AGAIN OUR LINE MATCHES THE LINE ON THE SCREEN.
LET'S TAKE A LOOK AT A COUPLE WHERE THEY'RE NOT SOLVED FOR Y.
IF WE WANT TO GRAPH THIS USING THE GRAPHING CALCULATOR,
WE DO HAVE TO SOLVE THIS EQUATION FOR Y.
SO WE WANT TO HAVE THIS LINE IN THE FORM OF Y EQUALS
AND THEN EVERYTHING ELSE ON THE RIGHT.
SO WE'LL START BY SUBTRACTING X ON BOTH SIDES,
SO WE HAVE -2Y = -X + 4.
NOW WE'LL DIVIDE EVERYTHING BY -2 TO SOLVE THIS FOR Y.
NOW WE NEED TO BE CAREFUL HERE.
THIS WOULD GIVE US Y ON THE LEFT.
NOW FOR THE -X YOU COULD WRITE -1X,
AND THAT'LL PROBABLY MAKE IT EASIER FOR US TO DETERMINE
THAT THE SLOPE WOULD BE -1/-2,
BUT A NEGATIVE DIVIDED BY A NEGATIVE IS POSITIVE,
SO WE'LL HAVE 1/2X AND 4 DIVIDED BY -2 IS -2.
SO WE'LL HAVE 1 1/2X - 2.
THIS IS THE FORM WE HAVE TO HAVE THE LINE IN
TO ENTER IT INTO THE CALCULATOR.
LET'S GO AHEAD AND TRY IT.
I'M GOING TO CLEAR THIS LINE, AND WE HAD Y = 1 1/2X - 2.
SO IN PARENTHESES WE'LL HAVE (1 DIVIDED BY 2) x (X - 2).
PRESS GRAPH.
AGAIN, THERE'S OUR LINE WHICH IS NICE,
BUT IT DOESN'T GIVE US EXACT POINTS TO PLOT
ON THE COORDINATE PLANE.
SO NOW WE'LL PRESS 2nd GRAPH.
AND AGAIN, TO AVOID DECIMAL VALUES OF Y,
WE'LL USE THE X COORDINATES THAT ARE MULTIPLES OF 2.
SO LET'S USE THE POINT (-2, -3) AND (0, -2).
SO (-2, -3) WOULD BE HERE.
LET'S ALSO USE THE POINT (0, -2) WHICH IS HERE.
AND LET'S GO AHEAD AND JUST USE ONE MORE.
LET'S PLOT THE POINT (2, -1), AND THAT WOULD BE HERE.
SO THERE'S OUR LINE.
AND SINCE WE TOOK THE TIME TO SOLVE IT FOR Y
AND PUT IT IN SLOPED INTERCEPT FORM,
NOTICE OUR Y-INTERCEPT IS -2.
OUR SLOPE IS 1/2, SO WE'LL GO UP 1, RIGHT 2.
SO IT LOOKS GOOD.
SO IT MAY OR MAY NOT BE EASIER TO GRAPH A LINE
ON THE GRAPHING CALCULATOR,
BUT IT IS A NICE WAY TO ALWAYS DOUBLE-CHECK YOUR WORK.
I HOPE YOU FOUND THIS VIDEO HELPFUL.