What is the equation of the line that passes through the point

Question

What is the equation of the line that passes through the point -7 and positive five that is parallel to the line 4X minus 7Y equals 28 right equation and slope intercept form

Answer 1

First, let's rewrite the given line in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.

Given equation: 4x−7y=28

Subtract 4x from both sides:

−7y=−4x+28

Divide both sides by -7:

y=4x/7​−4

So, the slope of the given line is m=4/7

Since the line we're trying to find is parallel to this line, it will have the same slope.

Now, we have the slopem=4/7​ and the point (−7,5)

Using the point-slope form of the equation of a line, which is y−y1​=m(x−x1​), where m is the slope and (x1​,y1​) is a point on the line, we can plug in the values we have:

y−5=4​(x+7)/7

Now, let's simplify and rewrite this equation in slope-intercept form:

y−5=4​x/7+28​/7

y=4​x/7+28/7​+35​/7

y=4​x/7+63​/7

So, the equation of the line that passes through the point (-7, 5) and is parallel to the line 4x−7y=28 in slope-intercept form is y=4​x/7+63​/7

Answer 2

Assuming the question is asking for the equation of a line that is parallel to 4x-7y=28 and passes through (-7,5):

First lets solve the given equation for y to put it into slope-intercept form.

-7y=28-4x

y=(4/7)x-4

Since we know the new line must be parallel to y=(4/7)x-4 we know the slope will stay the same at 4/7. And since we know it must intersect the point (-7,5) we can plug in all the data into y=mx+b to solve for b.

y=mx+b

5=(4/7)(-7)+b

5=-4+b

b=9

So the answer is y=(4/7)x+9