Question

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

Answer 1

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):

where:

• 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 b 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:

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

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

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