Write an equation in slope-intercept form for the line that satisfies each set of conditions.
29. Passes through (-2,5) and (3,1)
I already figured out the slope which is -4/5, but I can't figure out how to calculate the y-intercept. Can someone help me?
You must know that the slope y-intercept form of the equation takes the form
y = mx + b
and you said that the slope is -4/5 , so you know the equation must be
y = (-4/5)x + b
Why not just sub in (3,1) ? Wouldn't that leave b as your unknown ???
Just for fun, also sub in (-2,5) and see what happens.
Wait, could you please explain the process of that. This is the part where I get really confused. My textbook didn't explain it well.
(-2, 5), (3,1 ).
m = (1-5)/(3-(-2)) = -4/5.
Y = mx + b.
5 = (-4/5)*(-2) + b.
b = ?.
.
Eq: Y = (-4/5)x + b(use calculated value of b).
That would mean that b= -17/5. So my final answer would be: y = -4/5x - 17/5.
Thank you both for all your help. I now understand how to do it. :')
Glad we could help!
To find the equation of the line in slope-intercept form (y = mx + b), you have already found the slope (m) to be -4/5. Now, to determine the y-intercept (b), you can use one of the given points on the line, such as (-2,5).
Let's substitute the values (-2,5) into the equation y = mx + b, where m is the slope and b is the y-intercept:
5 = (-4/5)(-2) + b
Simplifying the equation gives:
5 = (8/5) + b
To isolate b, subtract (8/5) from both sides:
5 - (8/5) = b
Common denominators:
25/5 - 8/5 = b
Simplifying:
17/5 = b
Therefore, the y-intercept is b = 17/5.
The equation in slope-intercept form for the line that passes through (-2,5) and (3,1) is:
y = (-4/5)x + 17/5