My question is “The line passes through the points (-4.5, 2) and (6.3, 5.8).” I have to create an equation in y=mx+b form for these points. Can someone please help me. I don’t know how to solve this, because I wasn’t taught it. Please just give any help you can. Thank You!
y=mx+b You have one equation, two unknowns, and you have two solutions given, so, you can solve it. Start with the first point (-4.5, 2)
Y=mx+b
2=m(-4.5)+b
2=-4.5m+b Now the second point (6.3, 5.8)
5.8=6.3m+b Now you have two equations, two unknowns
2=m(-4.5)+b
5.8=6.3m+b
subtract the first equation from the second...
3.8=10.8m so you have m.
then put m into either equation, and solve for b
Thanks
or
slope = (5.8 - 2)/(6.3+4) = 3.8/10.8 = 19/54
so the equation is y = (19/54)x + b
sub in the "easiest point", namely (-4.5 , 2)
2 = (19/54)(-9/2) + b , -4.5 = -9/2
2 + 19/12 = b
b = 43/12
y = (19/54)x + 43/12
To find the equation of a line in the form y = mx + b, you will need to determine the slope (m) and the y-intercept (b) of the line.
To find the slope, you can use the formula:
m = (y2 - y1) / (x2 - x1)
Given the two points (-4.5, 2) and (6.3, 5.8), you can substitute the values into the slope formula:
m = (5.8 - 2) / (6.3 - (-4.5))
= 3.8 / 10.8
= 0.35185 (rounded to five decimal places)
Now that you have the slope (m), you can use one of the points and the slope to find the y-intercept (b).
Let's use the point (-4.5, 2):
y = mx + b
2 = (0.35185)(-4.5) + b
2 = -1.5833 + b
b = 2 + 1.5833
b = 3.5833 (rounded to four decimal places)
Now that you have the slope (m = 0.3519) and the y-intercept (b = 3.5833), you can write the equation of the line:
y = 0.3519x + 3.5833
Thus, the equation of the line passing through the points (-4.5, 2) and (6.3, 5.8) in the y = mx + b form is y = 0.3519x + 3.5833.