A line with a slope of m=−12

Question

m
=
−
1
2
passes through the point (4,6)
(
4
,
6
)
. What is the equation of the line in standard form?(1 point)
x+
x
+
y=
y
=

Answer 1

To find the equation of the line in standard form, we can start from the slope-intercept form of a line, which is:

\[ y = mx + b \]

Here, \( m = -\frac{1}{2} \) (the slope) and we need to find the y-intercept \( b \). We know the line passes through the point (4, 6).

Substituting \( x = 4 \) and \( y = 6 \) into the slope-intercept equation:

\[ 6 = -\frac{1}{2}(4) + b \]

Calculating the value on the right:

\[ 6 = -2 + b \]

Adding 2 to both sides:

\[ b = 6 + 2 = 8 \]

Now we have the equation in slope-intercept form:

\[ y = -\frac{1}{2}x + 8 \]

Next, we will convert this equation to standard form, \( Ax + By = C \). To achieve this, we can eliminate the fraction by multiplying the entire equation by 2:

\[ 2y = -x + 16 \]

Now, rearranging this equation to standard form, we add \( x \) to both sides:

\[ x + 2y = 16 \]

Thus, the equation of the line in standard form is:

\[ x + 2y = 16 \]