Question

Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD? y = 2x – 2 y = 2x + 2 y = x + 2 y = x – 2

Answer 1

Answer:  The correct option is (C) $y=x+2.$

Step-by-step explanation:  Given that the line CD passes through the points  (0, 2) and (4, 6).

We are to select the equation that represents line CD.

The slope of a straight line passing through the points (a, b) and (c, d) is given by

$m=\dfrac{d-b}{c-a}.$

So, the slope of  line CD is given by

$m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1.$

Since the line CD passes through the point (0, 2), so its equation will be

$y-2=m(x-0)\\\\\Rightarrow y-2=1\times x\\\\\Rightarrow y-2=x\\\\\Rightarrow y=x+2.$

Thus, the required equation of line CD is $y=x+2.$

Option (C) is CORRECT.

Answer 2

Slope = (6 - 2)/(4 - 0) = 4/4 = 1

y intercept (0,2) so b = 2

equation
y = x + 2

answer
y = x + 2