Question

Which is the correct slope-intercept equation for a line that passes through the points (1,-3) and (-3,17)

Answer 1

Answer:

$y=-5x+2$

Step-by-step explanation:

Hi there!

What we need to know:

• Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

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

Plug in the given points (1,-3) and (-3,17)

$=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5$

Therefore the slope of the line is -5. Plug this into $y=mx+b$:

$y=-5x+b$

2) Determine the y-intercept (b)

$y=-5x+b$

Plug in one of the given points and solve for b

$-3=-5(1)+b\\-3=-5+b$

Add 5 to both sides of the equation to isolate b

$-3+5=-5+b+5\\2=b$

Therefore, the y-intercept of the equation is 2. Plug this back into $y=-5x+b$:

$y=-5x+2$

I hope this helps!