How do you write an equation of a point slope form passing through (-5,4) and parallel to the line whose equation is #4x-7y-8=0#?

Answer 1

#y-4=4/7(x+5)#

#"we require to know that"#
#color(red)(bar(ul(|color(white)(2/2)color(black)("parallel lines have equal slope")color(white)(2/2)|)))#
#"the equation of a line in "color(blue)"slope-intercept form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))# where m represents the slope and b, the y-intercept.
#"rearrange " 4x-7y-8=0" into this form"#
#"subtract 4x from both sides"#
#cancel(4x)cancel(-4x)-7y-8=0-4x#
#rArr-7y-8=-4x#
#"add 8 to both sides"#
#-7ycancel(-8)cancel(+8)=-4x+8#
#rArr-7y=-4x+8#
#"divide ALL terms by -7"#
#(cancel(-7) y)/cancel(-7)=(-4)/(-7)x+8/(-7)#
#rArry=4/7x-8/7larr" in slope-intercept form"#
#rArr"slope "=m=4/7#
#"the equation of a line in "color(blue)"point-slope form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))# where # (x_1,y_1)" is a point on the line"#
#"using " m=4/7" and " (x_1,y_1)=(-5,4)" then"#
#y-4=4/7(x-(-5))#
#rArry-4=4/7(x+5)larrcolor(red)" in point-slope form"#
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Answer 2

To write the equation of a line in point-slope form passing through a given point and parallel to another line, follow these steps:

  1. Find the slope of the given line by rearranging its equation into slope-intercept form (y = mx + b), where m is the slope.
  2. Since the new line is parallel, it will have the same slope as the given line.
  3. Use the slope and the given point (-5, 4) to write the equation in point-slope form (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope.
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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.

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.

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.

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.

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