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OleMash [197]
3 years ago
13

What is the equation of the line that contains the points (0, 5) and (3, 7)?

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0

To find an equation of a line, you have to know the value of slope first. We can find the value of slope by using the formula below:

\large \boxed{m =  \frac{y_2 - y_1}{x_2 - x_1} }

m-term represents the slope from y = mx+b.

We are given two coordinate points. Substitute the points in the formula.

\large{m =  \frac{7 - 5}{3 - 0} } \\  \large{m =  \frac{2}{3} }

Therefore the slope is 2/3.

Next we find the y-intercept. In the form of y = mx+b where m = slope and b = y-intercept. We have got slope, except the y-intercept. We can find the y-intercept by substituting one of gjven points in the equation of y = mx+b.

Since we know the slope - we can rewrite the equation like below:

\large{y =  \frac{2}{3} x + b}

Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.

\large{5 =  \frac{2}{3} (0) + b} \\  \large{5 = 0 + b} \\  \large{b = 5}

Thus the y-intercept is (0,5). Note that if the question gives you (0,a) point. That is the y-intercept of graph. So b = a if given (0,a).

Rewrite the equation by substituting the b-value.

\large{y =  \frac{2}{3} x + 5}

Hence, the equation of a line that contains those points is y = 2x/3 + 5

Answer

  • y = 2x/3 + 5

Hope this helps! Let me know if you have any doubts.

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Find the difference between the 2 points.

For example, (8, 9) (5, 3).

Compare the difference between the x's, in this case 8 and 5. The difference is 3. Do the same with the y's, 9 and 3. The difference is 6.

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