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QuestionFind the value of bb in the line equation y=mx+by = mx + b for points C(1,3)C(1,3) and D(4,−3)D(4,-3).

Studdy Solution

STEP 1

Assumptions1. The line passes through points C(1,3) and D(4,-3). . The equation of the line is in slope-intercept form, y = mx + b.
3. We need to find the value of b, the y-intercept.

STEP 2

First, we need to find the slope (m) of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the coordinates of points C and D into the slope formula.
m=−3−3−1m = \frac{-3 -3}{ -1}

STEP 4

Calculate the slope.
m=−63=−2m = \frac{-6}{3} = -2

STEP 5

Now that we have the slope, we can use the point-slope form of the line equation to find the y-intercept (b). The point-slope form isy−y1=m(x−x1)y - y1 = m(x - x1)

STEP 6

Rearrange the point-slope form to the slope-intercept form (y = mx + b).
y=mx+(y1−mx1)y = mx + (y1 - mx1)

STEP 7

Now, plug in the values for the slope (m), and the coordinates of one of the points (for example, point C) into the rearranged equation.
y=−2x+(3−(−2∗1))y = -2x + (3 - (-2*1))

STEP 8

Calculate the y-intercept (b).
y=−2x+(3+2)y = -2x + (3 +2)y=−2x+5y = -2x +5So, the y-intercept (b) is5.

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