Question

Equation is y=1.5x+4 find an answer for:

Write an equation in standard form whose line is less steep and translated down 7 units.

Answer 1

6x -5y = 15

Explanation:

The given line has a slope of 1.5 and a y-intercept of 4. We assume that "translated down 7 units" means the y-intercept needs to be -3. "Less steep" will mean the slope is less than 1.5. We can make the slope be 1.2, so it will be less steep.

Then the slope-intercept form of the desired line is ...

y = 1.2x -3

Adding 3-y, this becomes ...

1.2x -y = 3

Multiplying this by 5 to put it into standard form, we have ...

6x -5y = 15

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Additional comment

Since the lines have different slopes, each point on the original line will be translated up or down by a different amount. We chose the y-intercept as the point to be translated by the specified amount. The question could be more clear on that point, as well as whether lines with negative slope (say, -2) are considered to be "less steep."