Answer:
The equation of line is: [tex]\mathbf{4x-3y=-18}[/tex]
Step-by-step explanation:
We need to find an equation of the line that passes through the points (-6, -2) and (-3, 2)?
The equation of line in slope-intercept form is: [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=-6,y_1=-2, x_2=-3, y_2=2[/tex]
Putting values and finding slope
[tex]Slope=\frac{2-(-2)}{-3-(-6)}\\Slope=\frac{2+2}{-3+6} \\Slope=\frac{4}{3}[/tex]
So, we get slope: [tex]m=\frac{4}{3}[/tex]
Finding y-intercept
Using point (-6,-2) and slope [tex]m=\frac{4}{3}[/tex] we can find y-intercept
[tex]y=mx+b\\-2=\frac{4}{3}(-6)+b\\-2=4(-2)+b\\-2=-8+b\\b=-2+8\\b=6[/tex]
So, we get y-intercept b= 6
Equation of required line
The equation of required line having slope [tex]m=\frac{4}{3}[/tex] and y-intercept b = 6 is
[tex]y=mx+b\\y=\frac{4}{3}x+6[/tex]
Now transforming in fully reduced form:
[tex]y=\frac{4x+6*3}{3} \\y=\frac{4x+18}{3} \\3y=4x+18\\4x-3y=-18[/tex]
So, the equation of line is: [tex]\mathbf{4x-3y=-18}[/tex]
