Given the equation:
[tex]\text{ y = 2x -6}[/tex]The equation is at Slope-Intercept Form: y = mx + b and the m in the equation represents the slope of the line. Therefore, the slope of the line that represents the equation y = 2x - 6 is 2.
It's been given that the equation of the line that we are looking for is parallel to y = 2x - 6 and passes through the point (3, -8). Thus, we will adapt the slope of the equation and determine the y-intercept by substituting the coordinates in the slope-intercept formula y = mx + b.
We get,
[tex]\text{ y = mx + b}[/tex]At slope, m = 2 and x,y = 3, -8:
[tex]-8\text{ = (2)(3) + b}[/tex][tex]-8\text{ = 6 + b}[/tex][tex]\text{ b = -8 - 6 = -14}[/tex]Let's substitute m = 2 and b = -14 to y = mx + b to complete the formula:
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (2)x + (-14)}[/tex][tex]\text{ y = 2x - 14}[/tex]Therefore, the equation of the line parallel to y = 2x - 6 and passes through (3, -8) is
y = 2x - 14.
