Question

Suppose a line, with a slope of -3 and a y-intercept of 4, is translated -4 units along the x-axis and 6 units along the y-axis. What is the equation of this new line?

pls hurry

Answer 1

Find equation of old line first

• m=-3
• b=4

Equation in slope intercept form

• y=-3x+4

Translated 4units left(x+4)

Translated 6 units up(y intercept +6)

Put it.

• y=-3(x+4)+6+4
• y=-3x-12+10
• y=-3x-2

Answer 2

y = -3x -2

Explanation:

The equation of the given line, with slope -3 and y-intercept 4, can be written in slope-intercept form as ...

y = -3x +4

When the line is translated by (h, k), it can be written as ...

(y -k) = -3(x -h) +4

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Here, we want to translate the line -4 in the x-direction and 6 in the y-direction. That is, (h, k) = (-4, 6). Using these values in the above equation, we have ...

y -6 = -3(x -(-4)) +4

y = -3x -12 +4 +6 . . . . simplify, add 6

y = -3x -2

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The attached graph shows the original line (red) with its y-intercept, and the translated line (green) with that y-intercept moved 4 units left and 6 units up.