Transcript for: Finding X and Y Intercepts of a Line
WE'RE GOING TO DETERMINE
THE INTERCEPTS OF THE LINE GIVEN THE EQUATION OF THE LINE WHICH MEANS WE WANT TO DETERMINE
THE X INTERCEPT AND THE Y INTERCEPT. AND WE CAN DO THIS BY COMPLETING
A SPECIAL TABLE OF VALUES TO DETERMINE THE X INTERCEPT. WE'RE GOING TO SET Y = 0
AND SOLVE FOR X. AND TO DETERMINE THE Y INTERCEPT
WE'LL SET X = 0 AND SOLVE FOR Y. SO BY COMPLETING
THIS SPECIAL TABLE OF VALUES WE CAN DETERMINE THE INTERCEPTS AND HOPEFULLY THIS MAKES SENSE BECAUSE IF WE TAKE A LOOK
AT THE X AXIS, EVERY Y COORDINATE
ALONG THE X AXIS IS EQUAL TO 0. AND THAT'S WHY TO DETERMINE
THE X INTERCEPT, WE SET Y = 0. AND THEN NOTICE EVERY POINT
ALONG THE Y AXIS THE X COORDINATE IS EQUAL TO 0. SO TO DETERMINE THE Y INTERCEPT,
WE SET X = 0 AND SOLVE FOR Y. LET'S GO AHEAD
AND DO THAT BELOW. LET'S START BY DETERMINING
THE X INTERCEPT. SO AGAIN WE'RE GOING TO DO THAT
Y EQUAL TO 0 AND SOLVE FOR X. SO IF WE LET Y = TO 0 NOTICE
HOW THIS -- HERE WOULD BE 0 SO WE'D BE LEFT WITH 2X = 5 THEN WE'D DIVIDE BOTH SIDES
BY 2. WE'D HAVE X = 5/2
WHICH WOULD BE OUR X INTERCEPT. SO AGAIN THE X INTERCEPT
IS THE POINT 5/2, 0 AND IT MIGHT ALSO BE HELPFUL
TO WRITE THIS AS A MIXED NUMBER OR A DECIMAL, 5/2 OR 5 DIVIDED BY 2 = 2.5. NOW WE'LL GO AHEAD AND DETERMINE
THE Y INTERCEPT AND AS I SAID BEFORE,
WE'RE GOING TO SET X = 0 AND SOLVE FOR Y. NOTICE IF WE SET X = 0,
2X SHOULD BE 0 SO WE'D BE LEFT
WITH THE EQUATION -Y = 5. AND IF IT'S HELPFUL WE CAN WRITE
THIS AS -1Y = 5 SO TO SOLVE FOR Y WE'LL DIVIDE
BY -1 SO WE HAVE Y = -5 SO WHEN X = 0, Y = -5, THEREFORE THE Y INTERCEPT
IS THE POINT 0, -5. NOW IT IS IMPORTANT THAT WE
DON'T LIST THE X INTERCEPT AS JUST X = 5/2 OR 2.5 BECAUSE TECHNICALLY THAT'S
THE EQUATION OF A VERTICAL LINE AND WE ALSO SHOULDN'T LIST
THE Y INTERCEPT AS JUST Y = -5 BECAUSE THAT'S AN EQUATION
OF A HORIZONTAL LINE. SO WE SHOULD EITHER GIVE
THE INTERCEPT AS ORDERED PAIRS OR STATE THE X INTERCEPT = 5/2
AND THE Y INTERCEPT = -5. NOW LET'S GO AHEAD
AND PLOT THE INTERCEPTS AND THEN SKETCH THE LINE. SO THE X INTERCEPT IS 5/2, 0
OR 2.50 SO THE X INTERCEPT WOULD BE HERE AND THEN THE Y INTERCEPT
IS THE POINT 0, -5 OR THIS POINT HERE. SO OUR LINE PASSES
THROUGH THESE TWO POINTS SO IT WOULD LOOK
SOMETHING LIKE THIS. OKAY THAT'S GOING TO DO IT
FOR THIS EXAMPLE. I HOPE YOU FOUND THIS HELPFUL.