find the equation of the line containing the given points (1,3) and (-3,-7). Express your answer in slope-intercept form.
Equation of the line. Slope-intercept
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(1,3) and (-3,-7)
The slope is defined as the change-of-y divided by the change-of-x...
Subtracting a negative number is the same as adding a positive number...
Let's take one point and apply the point-slope formula. This will expand into the slope-intercept formula. I randomly select the first point...
Let's add 3 to both sides...
This is slope-intercept format of...
y=mx+b, m is the slope and b is the y-intercept, the value of y when x=0.
Let's plug-in the other point to verify formula...
Slope intercept form is the form y= mx+b
where m is the slope and b is the y-intercept.
First, find your slope and plug into the form above
slope can be remembered as "rise over run." and your "rise" will be Y2-Y2 or 3-(-7) = 10
the "run" will be X2- X1 or 1 - (-3) = 4
therefore the slope is (Y2 - Y1 ) / (X2 - X1) = 10/4 or 2.5
Now plug into the slope intercept form using either of your original points. I picked the point (1,3)
y = mx + b
3 = (2.5)(1) + b now you must solve for b
3 = 2.5 + b and b = 0.5
Therefore the equation of the line is y = 2.5x + 0.5