G2a
Practice - X and Y Intercepts
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. You have the equation y = -16x² + 20x + 5. What is the y-intercept of this equation?
2. What is the y-intercept of y = 2x + 1? What is the x-intercept? What is the slope?
3. You have a straight line whose y-intercept is 5 and whose x-intercept is -3. What is the equation of the line?
4. Does a line have to have a y-intercept and an x-intercept?
5. What are the y- and x-intercepts of the equation 3y + 2x = 5?
ANSWERS
1. When x=0, the equation equals 5, which is the y-intercept.
2. With a linear equation in the form y = ax + b, you can read the slope and the y-intercept directly. The slope is a, or 2, and the y-intercept is b, or 1. To get the x-intercept, set y = 0. So 2x + 1 = 0, and 2x = -1, x = -½
3. Coordinates of the y-intercept are (0,5). Coordinates of the x-intercept are (-3,0). The slope is the difference of the y's divided by the difference of the x's, or (5-0)/(0+3) = 5/3. The equation is thus y - (5/3)x +5.
4. The line x = 3, for example, is always to the right of the y-axis and so never intercepts the y-axis. Similarly, the line y = 4 is always above the x-axis and so never intercepts it.
5. First you have to put the equation into slope/intercept form. Convert to 3y = -2x + 5, then to y = -(2/3)x + (5/3). With this you can see that when x = 0, y = (5/3). This is the y-intercept. When y = 0, (2/3)x = (5/3), so x = (5/3) x (3/2) = (5/2) = 2½. This is the x-intercept.
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