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How do you write an equation of a line parallel to #y=-3x+4# and x intercept at 4?

Answer 1

A parallel has the same slope, so the form is #y=-3x+b#

The #x#-intercept means #y=0and x=4# Use the equation: #0=-3*4+b# Add #3*4=12# to both sides: #12=cancel12-cancel12=b->b=12#

Equation: #y=-3x+12# graph{-3x+12 [-11.98, 16.5, -6.78, 7.46]}

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Answer 2

Avery Alexander

To write the equation of a line parallel to ( y = -3x + 4 ) with an x-intercept at 4, you know that parallel lines have the same slope. The slope of the given line is -3. Since the x-intercept is 4, you can substitute this value for x and solve for y to find the y-intercept. Then, you can use the slope and the y-intercept to write the equation of the parallel line.

Given the x-intercept at 4, substitute x = 4 into the equation: [ y = -3(4) + 4 ] [ y = -12 + 4 ] [ y = -8 ]

So, the y-intercept is -8.

Now, you have the slope (-3) and the y-intercept (-8), you can write the equation of the line in slope-intercept form: [ y = -3x - 8 ]

Therefore, the equation of the line parallel to ( y = -3x + 4 ) with an x-intercept at 4 is ( y = -3x - 8 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.