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pickupchik [31]
1 year ago
13

What is an Answer: equation of the line that passes through the points (-2, 7) and (-8, 4)?

Mathematics
2 answers:
Mariana [72]1 year ago
4 0
-2=x1 7=y1 -8=x2 4=y2

Y=Mx+b

Y2-y1 = 4-7 =-3
X2-x1 = -8-(-2) = -6
M (slope) = 3

Use the coordinate (-8, 4)

Y = MX + B = 4 = 3(-8) + b
4 = -24+ B
Add 24 to both sides to keep your equation balanced
B equals 28

Y = 3X + 28
kicyunya [14]1 year ago
3 0

Answer:

\sf \textsf{Equation:}\ y=\dfrac{1}{2}x+8

Step-by-step explanation:

The equation of the line can be written in slope-intercept form (y = mx + b):

<u>where:</u>

  • m is the slope
  • b is the y-intercept

To find the equation of a line when given two points, we first need to find the slope of the line.

The slope can be found using the following formula:

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

Given the points (-2, 7) and (-8, 4):

y₂ = 4, y₁ = 7

x₂ = -8, x₁ = -2

Substitute the values into the formula:

\sf m=\dfrac{4-7}{-8-(-2)}\ \textsf{[simplify]}\\\\m=\dfrac{4-7}{-8+2}\ \textsf{[simplify]}\\\\m=\dfrac{-3}{-6}=\dfrac{3}{6}\ \textsf{[reduce]}\\\\m=\dfrac{3\div3}{6\div3}\\\\m=\dfrac{1}{2}

Now, use one of the given points to solve for <u><em>b</em></u> by substituting the x and y-value into the equation:

\sf y=\dfrac{1}{2}x+b\\\\4=\dfrac{1}{2}(-8)+b\ \textsf{[multiply]}\\\\4=-4+b\ \textsf{[add 4 to both sides]}\\\\4+4=-4+4+b\\\\8=b

\sf \textsf{Equation of the line:}\ y=\dfrac{1}{2}x+8

Check your work:

\sf y=\dfrac{1}{2}x+8\\\\7=\dfrac{1}{2}(-2)+8\\\\7=-1+8\\\\7=7\ \checkmark

\sf \textsf{Therefore, our equation is:}\ y=\dfrac{1}{2}x+8

Learn more here:

brainly.com/question/24436844

brainly.com/question/27913172

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