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QuestionFind the equation of line CDC D that passes through points (0,2)(0,2) and (4,6)(4,6).

Studdy Solution

STEP 1

Assumptions1. Line CD passes through points (0,) and (4,6) . We are looking for the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept

STEP 2

First, we need to find the slope 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 the two points to calculate the slope.
m=6−2−0m = \frac{6 -2}{ -0}

STEP 4

Calculate the slope.
m=6−24−0=1m = \frac{6 -2}{4 -0} =1

STEP 5

Now that we have the slope, we can find the y-intercept (b) by substituting one of the points and the slope into the equation of the line.
b=y−mxb = y - mx

STEP 6

Plug in the values for the slope and one of the points (0,2) to calculate the y-intercept.
b=2−1⋅0b =2 -1 \cdot0

STEP 7

Calculate the y-intercept.
b=2−1⋅0=2b =2 -1 \cdot0 =2

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
y=mx+by = mx + b

STEP 9

Plug in the values for the slope and the y-intercept to write the equation of the line.
y=x+2y =x +2

STEP 10

implify the equation of the line.
y=x+2y = x +2The equation that represents line CD is y=x+2y = x +2.

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