Answer :
Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (2,1) and (4,5)
[tex]m=\frac{5-1}{4-2}\\m=\frac{4}{2}\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex] :
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in one of the given points and isolate b
[tex]1=2(2)+b\\1=4+b[/tex]
Subtract both sides by 4
[tex]1-4=4+b-4\\-3=b[/tex]
Therefore, the y-intercept of the line is -3. Plug this into [tex]y=2x+b[/tex]:
[tex]y=2x-3[/tex]
I hope this helps!
Answer:
y=2x-3
Step-by-step explanation:
Slope formula:
[tex]\sf{\dfrac{Y_2-Y_1}{X_2-X_1}[/tex]
y2=5
y1=1
x2=4
x1=2
Solve.
5-1/4-2
Subtract.
5-1=4
4-2=2
Divide.
4/2=2
The slope is 2.
You have to solve with slope-intercept form.
[tex]\sf{y=mx+b}[/tex]
m represents the slope.
b represents the y-intercept.
y-intercept is -3.
[tex]\sf{\boxed{y=2x-3}[/tex]
So, the correct answer is y=2x-3.