Answer:
[tex]8x + 5y = 11[/tex]
Step-by-step explanation:
First, to obtain the gradient we must rearrange the equation into the form [tex]y = mx + b[/tex], where [tex]m[/tex] is the gradient and [tex]b[/tex] is the y-intercept (the point where the line crosses the y-axis).
To rearrange to this form, take away [tex]8x[/tex] from both sides and divide by 5:
[tex]y = -\frac{8}{5}x + \frac{6}{5}[/tex]
From this equation, we can see the gradient is [tex]-\frac{8}{5}[/tex] and the y-intercept is [tex]\frac{6}{5}[/tex]
Now, to obtain the equation of the line parallel to [tex]8x + 5y = 6[/tex] we must find the new y-intercept. To do this, rearrange [tex]y = mx + b[/tex] to find [tex]b[/tex].
[tex]b = y - mx[/tex]
We know the value of [tex]m[/tex] from above ([tex]-\frac{8}{5}[/tex]), and the coordinates the line must pass through are in the question (2, -1).
We just put those values into the equation and solve for [tex]b[/tex]:
[tex]b = y - mx = (-1) - (- \frac{8}{5} )(2) = \frac{16-5}{5} = \frac{11}{5}[/tex]
Now, rearrange back to the original form and you obtain the answer:
[tex]8x + 5y = 11[/tex]
