Question

The graph of a line goes through the points (-4,3) and (6,8). What is the equation of the line in slope-intercept form?
Enter the correct answer in the box by replacing m and b with the appropriate values.
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7/3/2001

Answer 1

Answer:

$y=\frac{1}{2}x+5$

Step-by-step explanation:

Hi there!

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 lie on the line are $(x_1,y_1)$ and $(x_2,y_2)$

Plug the given points (-4,3) and (6,8) into the equation

$m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}$

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

$8=\frac{1}{2}(6)+b\\8=3+b$

Subtract 3 from both sides to isolate b

$8-3=3+b-3\\5=b$

Therefore, the y-intercept is 5. Plug this back into $y=\frac{1}{2}x+b$:

$y=\frac{1}{2}x+5$

I hope this helps!