Question

question 6 of 10, step 1 of 1 find the equation of the line which passes through the point (1, 2), and is parallel to the line with the equation ( y = -\frac{1}{2}x + 5 ). express your answer in slope - intercept form. simplify your answer.

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line is $y = -\frac{1}{2}x + 5$, so the slope $m = -\frac{1}{2}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = -\frac{1}{2}$, $x_1=1$, $y_1=2$.
$y - 2 = -\frac{1}{2}(x - 1)$

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y - 2 = -\frac{1}{2}x + \frac{1}{2}$
$y = -\frac{1}{2}x + \frac{1}{2} + 2$
$y = -\frac{1}{2}x + \frac{5}{2}$

Answer:

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