Question

find the slope - intercept form for the line passing through (5,4) and parallel to the line passing through (3,3) and (-5,1). the slope - intercept form for the line passing through (5,4) and parallel to the line passing through (3,3) and (-5,1) is y = (simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Calculate slope of reference line

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For points $(3,3)$ and $(-5,1)$:
$m = \frac{1 - 3}{-5 - 3} = \frac{-2}{-8} = \frac{1}{4}$

Step2: Use parallel slope for target line

Parallel lines have equal slopes, so target slope $m = \frac{1}{4}$. Use point-slope form $y - y_1 = m(x - x_1)$ with point $(5,4)$:
$y - 4 = \frac{1}{4}(x - 5)$

Step3: Convert to slope-intercept form

Expand and isolate $y$:
$y - 4 = \frac{1}{4}x - \frac{5}{4}$
$y = \frac{1}{4}x - \frac{5}{4} + 4$
$y = \frac{1}{4}x - \frac{5}{4} + \frac{16}{4}$
$y = \frac{1}{4}x + \frac{11}{4}$

Answer:

$y = \frac{1}{4}x + \frac{11}{4}$