Respuesta :

Recall that the slope intercept equation of a line is of the form y=mx+b where m is the slope and b is the y intercept. In general, two lines are parallel if they look like this

This translates to the fact the the lines never touch each other. This also means that, in a way, the lines increase (or decrease) at the same rate. This notion of rate of increase/decrease is captured by the fact that if we have lines y=m1x+b1 and y=m2x+b2 they are parallel if they have the same slope. That is

[tex]m_1=m_2[/tex]

We are given the line y=-3x+4 (with slope -3 and y intercept 4) and we want to find the equation y=mx+b. Since we want that both lines are parallel, based on our previous analysis, we should have

[tex]m=-3[/tex]

So, so far, our equation looks like this

[tex]y=-3x+b[/tex]

Now, we want this line to pass through the point (1,7), this means that whenever x=1, we must have y=7. So, we have the following equation

[tex]7=-3\cdot1+b[/tex]

If we add 3 on both sides, we get

[tex]b=7+3=10[/tex]

So our final result is the equation

[tex]y=-3x+10[/tex]

Ver imagen TimotheeX507547
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