G4a
Practice - From Algebra to Graphs
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. Draw the line representing the equation y = 3x + 6.
2. Graph the equation y -3x + 8 = 0.
3. Graph the equation 3x² + 4x - 6 = 0.
ANSWERS
1. The line crosses the y-axis at the point (0,6). Plot that point. The line crosses the x-axis when 0 = 3x + 6. Subtracting 6 from both sides gives 3x = -6, so x = -2. So the line crosses the x-axis at the point (-2,0). Draw the line between these two points. Since the equation is in the slope-intercept form, you can see immediately that the slope of the line is 3, which means that the line slopes upward to the right.
2. You could put this equation into slope-intercept form, but you don't have to. You can find the intercepts directly. First set x = 0, which makes the equation y + 8 = 0. Subtracting 8 from both sides gives y = -8, which is the y-intercept. Next set y = 0, which makes the equation -3x + 8 = 0. Adding 3x to both sides gives 3x = 8, or x = 8/3, which is the x-intercept. Plot the two points (0,-8) and (8/3,0) and draw the line between these two points.
3. This is a quadratic equation, because it contains an x² term. Therefore line of this equation is not a straight line, and is more complicated than what is covered here. If you encounter a test question like this, we urge you to guess quickly and move on, putting your test time into other questions.