Question

6 What is the equation in slope-intercept form of the line that passes through the points (-4, 2) and (12, 6)?
Q
H y = 4x + 18
y = 0.25x - 4.5
y = 4x - 42
F y = 0.25x + 3

Answer 1

To find the equation of the line that passes through the points \((-4, 2)\) and \( (12, 6)\), we first need to determine the slope \(m\) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1) = (-4, 2)\) and \((x_2, y_2) = (12, 6)\).

Substituting in the values:

\[
m = \frac{6 - 2}{12 - (-4)} = \frac{4}{12 + 4} = \frac{4}{16} = \frac{1}{4}
\]

Now that we have the slope \(m = \frac{1}{4}\), we can use the slope-intercept form of the equation of a line:

\[
y = mx + b
\]

To find \(b\) (the y-intercept), we can substitute one of the points into the equation. Let's use the point \((-4, 2)\):

\[
2 = \frac{1}{4}(-4) + b
\]

This simplifies to:

\[
2 = -1 + b
\]

Adding 1 to both sides gives:

\[
b = 3
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = \frac{1}{4}x + 3
\]

To match the form used in the options given, we can multiply the equation by 4 to eliminate the fraction:

\[
4y = x + 12
\]

Now, rearranging back to slope-intercept form gives:

\[
y = 0.25x + 3
\]

Thus, the correct equation in slope-intercept form is:

\[
\boxed{y = 0.25x + 3}
\]