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?

Answer 1

Answer:

$y=-3x-2$

Step-by-step explanation:

Slope-intercept form of a linear equation:  $y=mx+b$

where:

• $m$ is the slope
• $b$ is the y-intercept

Given:

• slope (m) = -3
• y-intercept (b) = 4

Equation of line: $y=-3x+4$

If the line is translated -4 units along the axis, we need to substitute

$x \rightarrow (x+4)$

If the line is translated 6 units along the y-axis, we need to add 6 to the equation:

$\implies y=-3(x+4)+4+6$

$\implies y=-3(x+4)+10$

$\implies y=-3x-12+10$

$\implies y=-3x-2$

Answer 2

Answer:

y = -3x - 2

Step-by-step explanation:

Rules to remember :

• f(x + a) = translated 'a' units left
• f(x - a) = translated 'a' units right

Standard form of the original equation

• y = mx + b
• here m = slope and b = y-intercept
• ⇒ y = -3x + 4

Translating -4 units along the x-axis

• y = -3(x + 4) + 4
• y = -3x - 12 + 4
• y = -3x - 8

Translating 6 units along the y-axis

• y = -3x - 8 + 6
• y = -3x - 2