Download Write or Identify a Linear Equation

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Generation Date: 02/22/2015
Generated By: Robert Dilliplane
1. Which of the following equations matches the graph below?
A.
B.
C.
D.
2. What is the slope of the line given by the following equation?
y = -5x + 4
A. -20
B. 4
C. -5
D. -1
3. A line with a slope of 1/3 passes through (-1,-2). Write the equation of the line in general form.
A. y + 2 = 1/3(x + 1)
B. x + 3y = 3
C. x - 3y = 5
D. y = 1/3x - 5/3
4.
A.
B.
C.
D.
5.
What is the slope of the line above?
A.
B.
C.
D.
6. Which of the following equations matches the graph below?
A.
B.
C.
D.
7. What is the slope of the line that passes through the points (2, -8) and (6, 2)?
A.
B.
C.
D.
8.
At what point does the line given by the following equation cross the y axis?
y = (-2/7)x + 1
A. (0, 1)
B. (0, 5/7)
C. (0, -2/7)
D. (1, 0)
10. A linear function has a y-intercept of 10 and a slope of
line?
A.
B.
C.
D.
. What is the equation of the
Answers
1. A
2. C
3. C
4. A
5. B
6. B
7. B
8. A
9. C
10. B
Explanations
1. All the answer choices are written in slope-intercept form, y = mx + b, where m is the slope
and b is the y-intercept.
The graph passes through the point (0,-3). Thus, the y-intercept is -3.
From the y-intercept (0,-3), move up 1 space and 2 spaces to the right to the point (2,-2). This
gives the following slope.
So, the equation of the line is given below.
2. The equation y = mx + b is called the slope-intercept form of a linear equation, where m is the
slope of the line and b is the y-intercept.
Therefore, the slope of the equation y = -5x + 4 is -5.
3. Plug the slope and point into the point-slope formula.
y - y1 = m(x - x1)
y - (-2) = 1/3(x - (-1))
y + 2 = 1/3(x + 1)
y + 2 = 1/3x + 1/3
(y + 2) × 3 = (1/3x + 1/3) × 3
3y + 6 = x + 1
0 = x + 1 - 3y - 6
0 = x - 3y - 5
x - 3y = 5
4. Use the point-slope form of an equation of a line to find the equation.
Substitute the point and slope into the equation.
5. The slope of a line is given by the equation below, where (x1, y1) and (x2, y2) are points on the
line.
So, find two points on the line, say (-4, 0) and (0, 2).
Substitute these points into the equation above to find the slope of the line.
Therefore, the slope of the line is
.
6. All the answer choices are written in slope-intercept form, y = mx + b, where m is the slope
and b is the y-intercept.
The graph passes through the point (0,1). Thus, the y-intercept is 1.
From the y-intercept (0,1), move up 1 space and 5 spaces to the right to the point (5,2). This
gives the following slope.
So, the equation of the line is given below.
7. Slope can be calculated using the following formula.
The rise is the change in the y-values, and the run is the change in the x-values.
Evaluate the formula using the given points.
Therefore, the slope is
.
8. The equation y = mx + b is called the slope-intercept form of a linear equation, where m is the
slope of the line and b is the y-intercept.
Given the equation of the line y = (-2/7)x + 1,
the y-intercept b = 1 and the line crosses the y-axis at the point (0, 1).
9. To find the equation, first find the slope of the line. For any two points (x1, y1) and (x2, y2), the
slope is given by the following.
Now, use one of the given points, the slope, and the point-slope form of an equation of a line.
10. Use the given information in the slope-intercept form of a line.