Answer :

absor201

Answer:

An equation for the line that has a rate of change of 2 and passes through the point (-1, -5) will be:

  • [tex]y=2x-3[/tex]

Step-by-step explanation:

As the equation for the line in the point-slop form is given by

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope (rate of change).

  • As we know that when we talk about 'slope', it means we are talking about 'rate of change'.

Now given the values

  • Rate of change = slope = m = 2
  • point (-1, -5)

substituting the values m = 2 and the point (-1, -5)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-5\right)=2\left(x-\left(-1\right)\right)[/tex]

[tex]y+5=2\left(x+1\right)[/tex]

[tex]y+5-5=2\left(x+1\right)-5[/tex]

[tex]y=2x-3[/tex]

Therefore, an equation for the line that has a rate of change of 2 and passes through the point (-1, -5) will be:

  • [tex]y=2x-3[/tex]
akposevictor

The equation of the line that passes through (-1, -5) and has a slope of 2 is;

  • [tex]\mathbf{y + 5 = 2(x + 1)}[/tex] (point-slope form)

or

  • [tex]\mathbf{y = 2x - 3}[/tex] (slope-intercept form)

Recall:

  • Equation of a line can be written either in the slope-intercept form as y = mx + c, or in point-slope form as y - b = m(x - a).
  • m = slope; c = y-intercept
  • Rate of change = slope

Given:

Slope (m) of the line is 2

Point on the line is (-1, -5)

Write the equation in point-slope form by substituting m = 2, and (a, b) = (-1, -5) into y - b = m(x - a).

Thus:

[tex]y - (-5) = 2(x - (-1))\\\\\mathbf{y + 5 = 2(x + 1)}[/tex]

Rewrite in slope-intercept form

[tex]y + 5 = 2x + 2\\\\y = 2x + 2 - 5\\\\\mathbf{y = 2x -3}[/tex]

Therefore, the equation of the line that passes through (-1, -5) and has a slope of 2 is;

  • [tex]\mathbf{y + 5 = 2(x + 1)}[/tex] (point-slope form)

or

  • [tex]\mathbf{y = 2x - 3}[/tex] (slope-intercept form)

Learn more here:

https://brainly.com/question/18359641

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