# Algebra 1 - 6.2 Homework, Part 1 (Slope-intercept Form)

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Determine the slope and y-intercept of a line; write the equation for a line in slope-intercept form given the slope and the y-intercept.

• 1.

### Find the slope and y-intercept of each equation.

• A.

M = 1/2, b = 2

• B.

M = -1/2, b = 2

• C.

M = 1/2, b = -2

• D.

M = -1/2, b = -2

B. M = -1/2, b = 2
Explanation
The slope of a line represents the rate of change of the line, or how steep it is. In this case, the slope is -1/2, which means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 1/2 unit. The y-intercept, represented by the variable b, is the point where the line intersects the y-axis. In this case, the y-intercept is 2, which means that the line crosses the y-axis at the point (0, 2). So, the equation of the line can be written as y = -1/2x + 2.

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• 2.

### Find the slope and y-intercept of each equation.

• A.

M = 5, b = 8

• B.

M = -5, b = 8

• C.

M = 5, b = -8

• D.

M = -5, b = -8

A. M = 5, b = 8
Explanation
The given answer states that the slope (m) is 5 and the y-intercept (b) is 8. In the equation of a line, the slope represents the rate of change of the line, while the y-intercept represents the point where the line intersects the y-axis. Therefore, the line represented by this equation has a slope of 5, indicating that for every unit increase in the x-coordinate, the y-coordinate increases by 5. The line intersects the y-axis at the point (0, 8), as indicated by the y-intercept value of 8.

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• 3.

### Find the slope and y-intercept of each equation.

• A.

M = 4, b = 0

• B.

M = -4, b = 0

• C.

M = 0, b = 4

• D.

M = 0, b = -4

B. M = -4, b = 0
Explanation
The given answer states that the slope (m) is -4 and the y-intercept (b) is 0. This means that the equation of the line can be written as y = -4x + 0, which simplifies to y = -4x. The slope of -4 indicates that the line has a negative slope, meaning it is decreasing as x increases. The y-intercept of 0 indicates that the line passes through the origin (0,0) on the y-axis.

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• 4.

### Find the slope and y-intercept of each equation.

• A.

M = 0.7, b = 9

• B.

M = -0.7, b = 9

• C.

M = 0.7, b = -9

• D.

M = -0.7, b = -9

D. M = -0.7, b = -9
Explanation
The given answer states that the slope (m) is -0.7 and the y-intercept (b) is -9. This means that the equation of the line can be written as y = -0.7x - 9. The negative slope indicates that the line is decreasing as x increases, and the negative y-intercept means that the line crosses the y-axis below the origin.

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• 5.

### Write an equation of a line with the given slope and y-intercept.

y = 2/9x + 3
y=2/9x+3
y = 2x/9 + 3
y=2x/9+3
y = 2/9 x + 3
Explanation
The equation of the line is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2/9 and the y-intercept is 3. Therefore, the equation of the line is y = 2/9x + 3.

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• 6.

### Write an equation of a line with the given slope and y-intercept.

y = 9/2x + 3
y=9/2x+3
y = 9x/2 + 3
y=9x/2+3
y = 9/2 x + 3
Explanation
The equation of a line is represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation y = 9/2x + 3 matches the form y = mx + b, where the slope is 9/2 and the y-intercept is 3. Therefore, the equation y = 9/2x + 3 is the correct answer.

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• 7.

### Write an equation of a line with the given slope and y-intercept.

y = -1x - 6
y=-1x-6
y = -x - 6
y=-x-6
Explanation
The equation of a line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the given equation y = -1x - 6 can be rewritten as y = -x - 6. This means that the slope is -1 and the y-intercept is -6. Therefore, the correct answer is y = -x - 6.

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• 8.

### Write an equation of a line with the given slope and y-intercept.

y = 0.3x + 4
y=0.3x+4
y = .3x + 4
y=.3x+4
Explanation
The equation of a line is typically written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the given equation y = 0.3x + 4 is already in the correct form. The slope of the line is 0.3 and the y-intercept is 4. Therefore, the equation of the line is y = 0.3x + 4.

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• 9.

### Write an equation of a line with the given slope and y-intercept.

y = -7x + 1/3
y=-7x+1/3
Explanation
The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation y = -7x + 1/3 has a slope of -7 and a y-intercept of 1/3. Therefore, the equation of the line is y = -7x + 1/3.

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• 10.

### Write an equation of a line with the given slope and y-intercept.

y = -1/4x + 5/4
y=-1/4x+5/4
y = -1x/4 + 5/4
y=-1x/4+5/4
Explanation
The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the given equation y = -1/4x + 5/4 is already in the correct form. The slope is -1/4 and the y-intercept is 5/4. Therefore, the equation of the line is y = -1/4x + 5/4.

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• 11.

### Write the slope-intercept form of the equation for each line.

y = -2/3x + 1
y=-2/3x+1
y = -2x/3 + 1
y=-2x/3+1
Explanation
The given answer options represent the slope-intercept form of the equation for a line. In the slope-intercept form, y = mx + b, "m" represents the slope of the line and "b" represents the y-intercept. In this case, the slope is -2/3 and the y-intercept is 1. Therefore, all four answer options correctly represent the equation in slope-intercept form.

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• 12.

### Write the slope-intercept form of the equation for each line.

y = 3/4x + 2
y=3/4x+2
y = 3x/4 + 2
y=3x/4+2
Explanation
The slope-intercept form of an equation for a line is y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, all four options are in the slope-intercept form. The equation y = 3/4x + 2 has a slope of 3/4 and a y-intercept of 2. Similarly, y=3/4x+2, y = 3x/4 + 2, and y=3x/4+2 all have the same slope and y-intercept. Therefore, all four options represent the equation of a line in slope-intercept form.

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• 13.

### Write the slope-intercept form of the equation for each line.

y = 4/2x - 2
y=4/2x-2
y = 2x - 2
y=2x-2
Explanation
The given answer provides the slope-intercept form of the equation for each line. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, all the equations have the same slope of 2 and the same y-intercept of -2. Therefore, all four equations represent the same line in the slope-intercept form.

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• 14.

### Write the slope-intercept form of the equation for each line. Estimate the y-intercept to the nearest 0.5

y = 2/4x + 0.5
y=2/4x+0.5
y = 1/2x + 0.5
y=1/2x+0.5
Explanation
The given answer is correct because it represents the slope-intercept form of the equation for each line. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In all the given equations, the slope is either 2/4 or 1/2, and the y-intercept is 0.5. Therefore, the answer y = 2/4x + 0.5, y=2/4x+0.5, y = 1/2x + 0.5, y=1/2x+0.5 is correct.

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• 15.

### Write the slope-intercept form of the equation for each line. Estimate the y-intercept to the nearest 0.5

y = -2/5x + 3
y=-2/5x+3
y = -2x/5 + 3
y=-2x/5+3
Explanation
The given answer is correct. The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -2/5 and the y-intercept is 3. Therefore, the correct answer is y = -2/5x + 3.

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• 16.

### Write the slope-intercept form of the equation for each line. Estimate the y-intercept to the nearest 0.5

y = 5/4x - 0.5
y=5/4x-0.5
y = 5x/4 - 0.5
y=5x/4-0.5
Explanation
The given equation is already in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The equation y = 5/4x - 0.5 has a slope of 5/4 and a y-intercept of -0.5. The other options are just different ways of writing the same equation.

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