Question

Write the equation of a line that is parallel to 3x+2y=10 and passes through the point (4,-5). Answer in slope-intercept form.

Answer 1

The equation of line is:

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

Further explanation:

The standard form of equation in point-slope form is:

$y = mx+b$

Given equation is:

3x+2y=10

We have to convert it into point slope form, for which we have to isolate y on one side of equation

$3x+2y = 10\\2y = -3x +10\\y = \frac{-3}{2}x + \frac{10}{2}\\y = \frac{-3}{2}x + 5$

Comparing with standard form:

m = -3/2

As the new line is parallel to given line, their slopes will be equal

So,

$y = \frac{-3}{2}x+b$

To find the value of b, putting the given point (4,-5) in equation

$-5 = \frac{-3}{2}(4)+b\\-5 = -6+b\\b = -5+6 \\b = 1\\So\ the\ equation\ is:\\y = \frac{-3}{2}x+1$

Keywords: Point-slope form, equation of line

Learn more about point-slope form of equation at:

• brainly.com/question/1577690
• brainly.com/question/1563227

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