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# Slope-intercept form of the equation of a line

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Write the slope-intercept form of the equation of each line (see the attached file).

Write the slope-intercept form of the equation of the line through the given points.

5) through: (-2, -3) and (0, 1)
6) through: (0, 2) and (-4, -3)
7) through: (0, 1) and (5, 3)
8) through: (0, -3) and (-1, -3)

https://brainmass.com/math/basic-algebra/slope-intercept-form-equation-line-612969

#### Solution Preview

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

The slope-intercept form of the equation of a line is

y = mx + b,

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

To find the slope of a line, we choose two points on that line, (x_1, y_1) and (x_2, y_2), and use the coordinates of those points to compute the slope:

slope = (y_2 - y_1)/(x_2 - x_1)

The y-intercept is the point that intersects the y-axis (equivalently, the point whose x-coordinate is 0, which the property that characterizes the points on the y-axis).

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1. The points (x_1, y_1) = (0, 4) and (x_2, y_2) = (-4, 1) are on this line. Thus the slope is

(y_2 - y_1)/(x_2 - x_1) = (1 - 4)/(-4 - 0) = (-3)/(-4) = 3/4.

The y-intercept is the point whose x-coordinate is 0. We have already found that point, namely (0, 4), and its y-coordinate is 4.

Thus m = 3/4 and b = 4, so the equation of this line is

y = (3/4)x + 4

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2. The points ...

#### Solution Summary

The slope and y-intercept of each line are computed, and these computations are explained in detail. Then they are used to write the slope-intercept form of the equation of the line.

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