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Write the equations of each line in slope-intercept form. (y=mx+b)

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Answer:

The equation would be y = -2x + 19

Explanation:

To find this, we can use the point and the slope in point-slope form. The we solve for y.

y - y1 = m(x - x1)

y - 7 = -2(x - 6)

y - 7 = -2x + 12

y = -2x + 19

User Lumialxk
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2 votes
To write the equation of a line in slope-intercept form, we need to determine the slope of the line and the y-intercept.

The slope-intercept form of the equation of a line is given by:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

To find the equation of a line in slope-intercept form, we need to determine the values of m and b.

Here are two examples:

The line passes through the points (2, 4) and (4, 8).
To find the slope, we use the formula:
m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (2, 4) and (x2, y2) = (4, 8)

m = (8 - 4)/(4 - 2) = 2

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is one of the points on the line, for example, (2, 4).

y - 4 = 2(x - 2)

y - 4 = 2x - 4

y = 2x + 0

Therefore, the equation of the line in slope-intercept form is y = 2x.

The line passes through the point (3, 7) and has a slope of -3.
We can use the point-slope form of the equation of a line to find the equation in slope-intercept form.
y - y1 = m(x - x1)

where (x1, y1) is the given point, (3, 7), and m is the slope, which is -3.

y - 7 = -3(x - 3)

y - 7 = -3x + 9

y = -3x + 16

Therefore, the equation of the line in slope-intercept form is y = -3x + 16
User Daniel Sloof
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