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A line passes through the point (-3,4) and has a slope of -5. Find an equation of this line

Sagot :

amysun2025

Answer:

y = -5x - 11

Step-by-step explanation:

We are given that a line passes through the point (-3,4) and also has a slope of -5.

We want to write an equation of this line.

The equation of the line can be written in 3 different ways:

  • Slope-intercept form, which is written as y=mx+b, where m is the slope and b is the y intercept.
  • Standard form, which is written as ax+by=c, where a, b, and c are free integer coefficients (but a and b cannot be 0, and a cannot be negative).
  • Slope-point form, which is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope, and [tex](x_1, y_1)[/tex] is a point

Since the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.

Because we are already given the value of the slope, we can immediately plug that into the equation.

Replace m with -5.

y = -5x + b

Now we need to find b.

As the equation passes through the point (-3, 4), we can use its values to help solve for b.

Substitute -3 as x and 4 as y.

4 = -5(-3) + b

Multiply

4 = 15 + b

Subtract 15 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = -5x - 11

Topic: finding the equation of the line

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