Test Name: Chapter 3 Review 1. For the following equation, determine the values of the missing entries. If needed, write your answer as a fraction reduced to lowest terms. 10x - 8y = 18 Note: Each column in the table represents an ordered pair. x 0 3 y 0 4 2. Identify the quadrant or axis that the following point lies on. If the point lies on an axis, specify which part (positive or negative) of which axis (x or y). (-6 3 ) A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV E) Axis A) Positive-x B) Positive-y C) Negative-x D) Negative-y 3. Consider the following equation of a line. 2x + 3y = 2y - 7 Step 1. Rewrite this equation in slope-intercept form. Reduce all fractions to lowest terms. Step 2. Find the equation, in slope-intercept form, for the line which is perpendicular to this line and passes through the point (-4-9). Reduce all fractions to lowest terms. 4. Find the standard form of the equation for the circle described below. Center -9-4 3 and tangent to the y-axis 5. Find the standard form of the equation for the circle described below. Center (-4-4), passes through ( 6 8 ) 1
6. Consider the following equation. -12x = -12y Step 1. Determine the x- and y-intercepts of the given equation, if possible. If one of the intercepts does not exist, state "absent" for that intercept. -intercept: (, ) OR -intercept: (, ) OR Step 2. Graph the given equation by plotting the x- and y-intercepts on the graph below, if possible. If an intercept does not exist, use another point to plot the graph. 2
7. Consider the equation below. Step 1. Find the center ( h k ), of this circle. ( x + 2) 2 + ( y - 5) 2 = 9 Step 2. Find the radius, r, of this circle. Step 3. Graph the circle. 8. For the following equation, determine the values of the missing entries. If needed, write your answer as a fraction reduced to lowest terms. y = x 2-14x + 49 Note: Each column in the table represents an ordered pair. If multiple solutions exist, select either one to enter in the box. x 6 10 5 y 0 1 9. Consider the following equation of a line. Reduce all fractions to lowest terms. 6y - 11 = - 2( 2 - x ) Step 1. Rewrite this equation in slope-intercept form. Step 2. Find the equation, in slope-intercept form, for the line which is parallel to this line and passes through the point (-7 3 ). 3
10. Find the standard form of the equation for the circle graphed to the left. 11. Consider the following pair of points: Step 1. Determine the distance between the two points. ( 9-6) and (-3-8) Step 2. Determine the midpoint of the line segment joining the pair of points. 12. Write the standard form of the equation for the line that passes through the points ( 3-6 ) and ( 0-6 ). 13. Consider the following equation of a line. 7( y + x ) - 4( x - y ) = -8 Step 1. Rewrite this equation in slope-intercept form. Reduce all fractions to lowest terms. Step 2. Find the equation, in slope-intercept form, for the line which is perpendicular to this line and passes through the point (-6-9). Reduce all fractions to lowest terms. 4
14. Consider the following linear equation: -5x + 4y = 31 Step 1. Determine the slope and y-intercept of the equation above. If the slope is undefined, state "undefined": slope = A) Undefined y-intercept = (, ) Step 2. Graph the point on the line with x = -3. [Continued on Next Page...] 5
Step 3. Graph the point on the line with x = 1. 15. Consider the following equation. 4y + 3x = 4y + 6 Step 1. Determine the x- and y-intercepts of the given equation, if possible. If one of the intercepts does not exist, state "absent" for that intercept. -intercept: (, ) OR -intercept: (, ) OR Step 2. Graph the given equation by plotting the x- and y-intercepts on the graph below, if possible. If an intercept does not exist, use another point to plot the graph. 6
16. Find the slope of the line determined by the equation 3y + 7 = -5x. Please write your answer in simplest form. If the slope is undefined state "Undefined". 17. Consider the following equation. Step 1. Write the equation in slope-intercept form. x - 3y = 1 Step 2. Given x = 4, find the value for y and graph the ordered pair. y = Step 3. Given x = 7, find the value for y and use the point to complete the graph of the line. y = 7
18. Consider the following equation. 3y + 7x = 7( 3 + x ) Step 1. Determine the x- and y-intercepts of the given equation, if possible. If one of the intercepts does not exist, state "absent" for that intercept. -intercept: (, ) OR -intercept: (, ) OR Step 2. Graph the given equation by plotting the x- and y-intercepts on the graph below, if possible. If an intercept does not exist, use another point to plot the graph. 8
19. Consider the equation below. Step 1. Find the center ( h k ), of this circle. x 2 + y 2 + 4x - 20y = -88 Step 2. Find the radius, r, of this circle. Step 3. Graph the circle. 9