Answer:
The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]
Step-by-step explanation:
Determine the equation of the line that goes through points (1,1) and (3,7)
We can write the equation of line in slope-intercept form [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
We need to find slope and y-intercept.
Finding Slope
Slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=1, y_1=1, x_2=3, y_2=7[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3[/tex]
We get Slope = 3
Finding y-intercept
y-intercept can be found using point (1,1) and slope m = 3
[tex]y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2[/tex]
We get y-intercept b = -2
So, equation of line having slope m=3 and y-intercept b = -2 is:
[tex]y=mx+b\\y=3x-2[/tex]
The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]
