Topic 2: MathXL for School: Topic Review

If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, [tex] y = mx + b [/tex]. Using the coordinates of the given point, determine the value of [tex] b [/tex].

Using the above technique, find the equation of the line containing the points (-4, 20) and (2, -1).

The equation of the line is [tex] y = -x + 6 [/tex].

(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

To find the equation of a line given the slope and a point on the line, use the slope-intercept form y=mx+b. Substitute the slope and the coordinates of a point into the equation to find the value of b.

Explanation:

To find the equation of a line when the slope and a point on the line are known, we can use the slope-intercept form, y=mx+b. For example, let's find the equation of the line containing the points (-4,20) and (2,-1). First, calculate the slope using the formula: m = (y2-y1)/(x2-x1). So, m = (-1-20)/(2-(-4)) = -21/6 = -7/2. Now we can substitute the slope (-7/2) and the coordinates of one of the points into the slope-intercept form to find the value of b. Let's choose the point (-4,20). The equation becomes 20 = (-7/2)(-4) + b. Simplifying, 20 = 14 + b. Subtracting 14 from both sides, we get b = 20 - 14 = 6. Therefore, the equation of the line is y = (-7/2)x + 6.

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