Answer:
[tex]{y=\frac{1}{2}x+\frac{5}{2}[/tex]
Step-by-step explanation:
We can write the equation in slope intercept form.
[tex]y=mx+b[/tex]
Finding Slope:
Slope is (rise/run). [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,2) and (3,4).
[tex]\frac{4-2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]
The slope is 1/2.
Finding Y-intercept:
We can use the equation [tex]y=\frac{1}{2}x+b[/tex] to solve for the y-intercept.
Replace 'y' and 'x' with a given point and solve for 'b'. I will use (3,4).
[tex]4=\frac{1}{2}(3)+b\\\\4=\frac{3}{2}+b\\\\\frac{3}{2}+b=4\\\\\frac{3}{2}-\frac{3}{2}+b= 4-\frac{3}{2}\\\\[/tex]
[tex]b=\frac{5}{2}[/tex]
The y-intercept is 5/2.
Final Equation:
As stated above, slope intercept form is [tex]y=mx+b[/tex]. 'M' is the slope and 'b' is the y-intercept.
We are given the slope of 1/2 and the y-intercept of 5/2.
[tex]y=mx+b\rightarrow\huge\boxed{y=\frac{1}{2}x+\frac{5}{2}}[/tex]
