Question

please write the equation of each line in slope point form, and general form please!!
1.passes through (-5,4) and is perpendicular to y=5/7x+4
2.passes through (-1,4), parallel to y=-4x-5
3.passes through(-2,-3) parallel to y=-1/2x+4
4.passes through(-2-3) perp. to y=-1/3x+2

Answer 1

Remember what perpendicular tells us?
It's telling us that the slope of our new line will be the `negative reciprocal` of the original.

In part 1, the line we're compared to has a slope of \(\large \dfrac{5}{7}\).
The slope of our new line will be the `negative reciprocal` of this value, or in other words \(\large -\dfrac{7}{5}\).

In general form, we can write our new line like this.\[\large y=-\frac{7}{5}+b\]From here, we can solve for \(\large b\), our y-intercept, by using the coordinate pair that they gave us.