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yulyashka [42]
2 years ago
6

Write an equation in slope-intercept form for the following line: (-17,-4) and (-7,-13)

Mathematics
1 answer:
Wittaler [7]2 years ago
7 0
<h2>Slope-intercept form</h2>

Linear equations are often organized in slope-intercept form:

y=mx+b

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

<h3>Slope (m)</h3>

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

  • <em>"Rise"</em> refers to the number of units the line travels up.
  • <em>"Run"</em> refers to the number of units the line travels to the right.

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

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

<h3>Y-intercept (b)</h3>

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.

<h2>Writing the Equation</h2>

1) Determine the slope of the line (m)

m=\dfrac{y_2-y_1}{x_2-x_1}

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

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

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

y=-\dfrac{9}{10}x+b

2) Determining the y-intercept (b)

y=-\dfrac{9}{10}x+b

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

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

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

y=-\dfrac{9}{10}x-\dfrac{193}{10}

<h2>Answer</h2>

y=-\dfrac{9}{10}x-\dfrac{193}{10}

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