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Write the equation of the line that has a rate of change of 5 and passes through the point

(4, -1)

2 Answers

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The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

We are given that the rate of change (slope) is 5 and that the line passes through the point (4, -1).

Substituting the values into the point-slope form, we get:

y - (-1) = 5(x - 4)

Simplifying the equation, we get:

y + 1 = 5x - 20

y = 5x - 21

Therefore, the equation of the line that has a rate of change of 5 and passes through the point (4, -1) is y = 5x - 21.
User Harvinder
by
8.2k points
3 votes

Hello

Answer:


\Large \boxed{\sf y=5x-21}

Explanation:

The slope-intercept form of a line equation is
\sf y=mx+b where m is the rate of change (or the slope) and b is the y-intercept.

We know that the rate of change is 5 so :
\boxed{\sf m=5}


\sf y=5x+b

Let's find the value of b !

Moreover, we know that the line passes through the point (4,-1).

Let's replace x and y with 4 and -1 in the equation and solve for b:


\sf -1=4*5+b


\sf\iff -1=20+b

Let's substract 20 from both sides :


\sf -1-20=20-20+b


\boxed {\sf b=-21}

The equation of the line is :
\boxed{\sf y=5x-21}

Have a nice day ;)

User Werulz
by
8.3k points

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