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forsale [732]
2 years ago
6

A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.

Mathematics
1 answer:
slava [35]2 years ago
5 0

We have been given that a line y=mx+b passes through the point (10, 3) and is parallel to the line 2x+5y=12. We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

2x-2x+5y=12-2x

5y=-2x+12

\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}

y=-\frac{2}{5}x+\frac{12}{5}

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be -\frac{2}{5}.

Now we will use slope-intercept form of equation to find y-intercept.

y=mx+b, where,

m = Slope,

b = The y-intercept.

Let us substitute m=-\frac{2}{5} and coordinates of point (10,3) in above equation as:

3=-\frac{2}{5}(10)+b

3=-2(2)+b

3=-4+b

3+4=-4+4+b

7=b

Therefore, the y-intercept is 7 and our required equation would be y=-\frac{2}{5}x+7.

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