4-7 HW Handout Algebra With Pizzazz P. 159 And P. 160

1) #7, p. 159.Write the equation in point-slope form of the line with slope

minus 2 over 3

and passing through (3, 4).

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Explanation

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2) #4, p. 159.Write the equation in point-slope form of the line with slope 3 and passing through (‒4, ‒7).

Y ‒ 7 = 3(x ‒ 4)

Y + 7 = 3(x + 4)

Y + 4 = 3(x + 7)

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The equation y + 7 = 3(x + 4) is the correct answer because it represents the point-slope form of a line. In this form, the slope of the line is represented by the coefficient of x, which is 3 in this case. The point (‒4, ‒7) is used to determine the y-intercept of the line, which is represented by the constant term in the equation. The equation is consistent with the given slope and passes through the given point, making it the correct answer.

Explanation

The equation y + 7 = 3(x + 4) is the correct answer because it represents the point-slope form of a line. In this form, the slope of the line is represented by the coefficient of x, which is 3 in this case. The point (‒4, ‒7) is used to determine the y-intercept of the line, which is represented by the constant term in the equation. The equation is consistent with the given slope and passes through the given point, making it the correct answer.

3) #11, p. 159.Write the equation in point-slope form of the line with slope ‒2 and passes through (0, 0).

Y ‒ 0 = 0(x ‒ 0)

Y + 2 = 0(x + 2)

Y ‒ 2 = 0(x ‒ 2)

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The given equation in point-slope form is y - 2 = 0(x - 2). This equation represents a line with a slope of 0 and passes through the point (2, 2).

Explanation

The given equation in point-slope form is y - 2 = 0(x - 2). This equation represents a line with a slope of 0 and passes through the point (2, 2).

4) #7, p. 160Find the equation in slope-intercept form of the line that passing through (4, 1) and (‒4, 7).

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The equation in slope-intercept form of a line can be found using the formula y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values (4, 1) and (-4, 7), we get a slope of -6/8 or -3/4. To find the y-intercept, we can substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b. Using the point (4, 1), we get 1 = (-3/4)(4) + b, which simplifies to 1 = -3 + b. Solving for b, we get b = 4. Therefore, the equation in slope-intercept form is y = (-3/4)x + 4.

Explanation

The equation in slope-intercept form of a line can be found using the formula y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values (4, 1) and (-4, 7), we get a slope of -6/8 or -3/4. To find the y-intercept, we can substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b. Using the point (4, 1), we get 1 = (-3/4)(4) + b, which simplifies to 1 = -3 + b. Solving for b, we get b = 4. Therefore, the equation in slope-intercept form is y = (-3/4)x + 4.

5) #2, p. 160Find the equation in slope-intercept form of the line that passing through (0, 1) and (3, ‒8).

Y = ‒x + 1

Y = 2x + 1

Y = ‒3x +1

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (0, 1) and (3, -8). Plugging these values into the formula, we get (-8 - 1) / (3 - 0) = -9 / 3 = -3. So the slope of the line is -3. Since the line passes through the point (0, 1), we can substitute these values into the equation and solve for the y-intercept b. Plugging in x = 0 and y = 1, we get 1 = -3(0) + b, which simplifies to b = 1. Therefore, the equation of the line is y = -3x + 1.

Explanation

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (0, 1) and (3, -8). Plugging these values into the formula, we get (-8 - 1) / (3 - 0) = -9 / 3 = -3. So the slope of the line is -3. Since the line passes through the point (0, 1), we can substitute these values into the equation and solve for the y-intercept b. Plugging in x = 0 and y = 1, we get 1 = -3(0) + b, which simplifies to b = 1. Therefore, the equation of the line is y = -3x + 1.