Question

Write the equation of a line that passes through the points ( 2 , - 5 ) and ( 8 , - 2 )

Answer 1

Answer:

$y=\frac{1}{2}x-6$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

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

Plug in the given points (2,-5) and (8,-2)

$m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-(-5)}{8-2}\\=\frac{-2+5}{8-2}\\=\frac{3}{6}\\=\frac{1}{2}$

Therefore, the slope of the line is $\frac{1}{2}$. Plug this into $y=mx+b$:

$y=\frac{1}{2}x+b$

2) Determine the y-intercept (b)

$y=\frac{1}{2}x+b$

Plug in one of the given points and solve for b

$-5=\frac{1}{2}(2)+b\\-5=1+b$

Subtract 1 from both sides to isolate b

$-5-1=1+b-1\\-6=b$

Therefore, the y-intercept of the line is -6. Plug this back into $y=\frac{1}{2}x+b$:

$y=\frac{1}{2}x+(-6)\\y=\frac{1}{2}x-6$

I hope this helps!