Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Write an equation in slope-intercept form for the following line:

(-17,-4) and (-7,-13)

Sagot :

theleangreenbean

Slope-intercept form

Linear equations are often organized in slope-intercept form:

[tex]y=mx+b[/tex]

  • (x,y) = a point that falls on the line
  • m = the slope of the line
  • b = the y-intercept of the line

Slope (m)

The slope of a line is equal to its [tex]\dfrac{rise}{run}[/tex].

  • "Rise" refers to the number of units the line travels up.
  • "Run" refers to the number of units the line travels to the right.

Typically, we would solve for the slope by using the following formula:

  • [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Y-intercept (b)

The y-intercept of a line refers to the y-value that occurs when x=0.

On a graph, it is the y-value where the line crosses the y-axis.

Writing the Equation

1) Determine the slope of the line (m)

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Plug in the two given points, (-17,-4) and (-7,-13):

[tex]m=\dfrac{-13-(-4)}{(-7)-(-17)}\\\\m=\dfrac{-13+4}{-7+17}\\\\m=\dfrac{-9}{10}[/tex]

Therefore, the slope of the line is [tex]-\dfrac{9}{10}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-\dfrac{9}{10}x+b[/tex]

2) Determining the y-intercept (b)

[tex]y=-\dfrac{9}{10}x+b[/tex]

Plug in one of the given points and solve for b:

[tex]-4=-\dfrac{9}{10}(-17)+b\\\\-4=\dfrac{153}{10}+b\\\\b=-\dfrac{193}{10}[/tex]

Therefore, the y-intercept of the line is [tex]-\dfrac{193}{10}[/tex]. Plug this back into our equation:

[tex]y=-\dfrac{9}{10}x-\dfrac{193}{10}[/tex]

Answer

[tex]y=-\dfrac{9}{10}x-\dfrac{193}{10}[/tex]

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.