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# how do you write the equation of a line in slop intercept form, given two ponts that the line passes through?

how do you write the equation of a line in slop intercept form, given two ponts that the line passes through? Also how do you find the line parallel and perpendicular to it?

my homework says:

a.) explain how to write the equation of a line in slope intercept form that passes through (-3, -1) and (6, -4)

b.) Explain how to write the equation of a line that passes through (-6,2) and is parallel to the line in part a

c.) Explain how to write the equation of a line that passes through (-1,2) and is perpendicular to the line in part a

help would be very appreciated. Its my teachers first year and he isnt really the best at teaching, ive asked him numerous times on how to do it but i still cant understand it

### 2 réponses

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Slope intercept form is like this

y= mx+b

m is the slope

b is the y intercept (where the line crosses the y axis)

To find slope---- Rise/Run (Change in y divided by change in x)

For example if you have points (4,7) and (-3,9)

Slope would be -2/7 (where the minus sign on slope doesn't matter)

To answer a) You need point slope formula. This allows you to find the y intercept if you have the slope. The formula is

y – y1 = m(x – x1) y1 is would be -1 in your problem

m is slope remember

b) If a line is parallel it means it has the same slope as the other one. Then use point slope formula to find the equation.

c) Perpindicular lines are the opposite reciprocal of eachother's slopes. This means the a slope of -3/4 becomes 4/3 (opposite means switch the sign, reciprocal means flip the numbers)

Here I'm assuming you know how to distribute numbers across a parenthesis like 3(x+3) = 3x+9