Question

write an equation of the line that passes through \\((3, 2)\\) and is parallel to the line defined by \\(-3x = 4y + 2\\). write the answer in slope-intercept form (if possible) and in standard form (\\(ax + by = c\\)) with smallest integer coefficients. use the \cannot be written\ button, if applicable.

part 1 of 2
the equation of the line in slope-intercept form:

part 2 of 2
the equation of the line in standard form:

Explanation:

Step 1: Find the slope of the given line.

$$-3x = 4y + 2 \implies 4y = -3x - 2 \implies y = -\frac{3}{4}x - \frac{1}{2}$$

Step 2: Determine the parallel line's slope.

$$m = -\frac{3}{4}$$

Step 3: Use point-slope form with point \((3, 2)\).

$$y - 2 = -\frac{3}{4}(x - 3)$$

Step 4: Convert to slope-intercept form.

$$y = -\frac{3}{4}x + \frac{9}{4} + 2 \implies y = -\frac{3}{4}x + \frac{17}{4}$$

Step 5: Convert to standard form.

$$4y = -3x + 17 \implies 3x + 4y = 17$$

Answer:

Part 1: \(y = -\frac{3}{4}x + \frac{17}{4}\)
Part 2: \(3x + 4y = 17\)