Question

Determine the equation of the line that goes through points (1.1) and (3.7).

Answer 1

Answer:

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

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 $y=mx+b$ 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: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=1, y_1=1, x_2=3, y_2=7$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3$

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

$y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2$

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

$y=mx+b\\y=3x-2$

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$