Question

Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14) as follows.

m = StartFraction 14 minus (negative 2) Over 3 minus (negative 5) EndFraction = StartFraction 16 Over 8 EndFraction = 2. y = 2 x + b. Negative 2 = 2 (negative 5) + b. Negative 2 + 10 = negative 10 + b + 10. b = 8.


What is the equation of the line in slope-intercept form?
y = 2 x minus 8
y = 2 x + 8
y = 8 x minus 2
y = 8 x + 2

Answer 1

Mike's calculations appear to contain some errors when solving for the y-intercept \( b \). Let's break it down correctly to find the equation of the line.

1. **Calculate the slope \( m \)**:
\[
m = \frac{14 - (-2)}{3 - (-5)} = \frac{14 + 2}{3 + 5} = \frac{16}{8} = 2
\]

2. **Find the y-intercept \( b \)** using one of the points; let's use the point \((-5, -2)\):
\[
y = mx + b
\]
Substituting the known values:
\[
-2 = 2(-5) + b
\]
\[
-2 = -10 + b
\]
\[
b = -2 + 10 = 8
\]

3. **Write the equation in slope-intercept form \( y = mx + b \)**:
\[
y = 2x + 8
\]

Thus, the correct equation of the line in slope-intercept form is:
\[
\boxed{y = 2x + 8}
\]