Question

write the slope-intercept form of the equation for the line that passes through (4,9) and is parallel to the graph of the equation 5x-4y=8

Answer 1

y=1.25x+4

Explanation:

• Two equations are paralell if they have the same slope.
• Then to find the paralell equation to
  `5x-4y=8`, we can do the following: clear out y as a function of x, to get the intercept and the slope that accompanies x.
• To do this, we follow the next steps: 1) subtract 5x both sides of the equation (which results in
  `-4y=8-5x`; 2) divide both sides by (-4), would yield
  `y=1.25x-2`.
• Now we have an clear expression of y as a function of x, and can find a parallel line that passes through (x,y)=(4,9). This new equation shall be an expression that meets the following: 9=1.25 (4)+h, where we do not know the value of h, and the values of (x,y) have been replaced by the point required.
• If we solve the equation above, we obtain the value of h (intercept) for our parallel equation: h=4.
• Then, the parallel equation that passes through (4,9) is y=1.25x+4 (to verify this is ok, replace x=4 in this equation, and you will get y=9, which is what we were lloking for: a parallel equation to y=1.25x-2 that passes through (4,9)