Question

Which represents the equation of the line that
passes through the points (5,-2) and (15, 6)?

Answer 1

Answer:

$y =\frac{4}{5}x-6$

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 given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (5,-2) and (15, 6)

$=\frac{6-(-2)}{15-5}\\=\frac{6+2}{15-5}\\=\frac{8}{10}\\=\frac{4}{5}$

Therefore, the slope of the line is $\frac{4}{5}$. Plug this into $y =mx+b$:

$y =\frac{4}{5}x+b$

2) Determine the y-intercept (b)

$y =\frac{4}{5}x+b$

Plug in one of the given points and solve for b

$6=\frac{4}{5}(15)+b\\6=12+b$

Subtract 12 from both sides of the equation to isolate b

$6-12=12+b-12\\-6=b$

Therefore, the y-intercept of the line is -6. Plug this back into $y =\frac{4}{5}x+b$:

$y =\frac{4}{5}x-6$

I hope this helps!