Write the slope-intercept form of the equation of the line described. 15) through: (4,-1) parallel to y=-(3)/(4)x 16) through: (4,5) parallel to y=(1)/(4)x-4 17) through: (-2,-5) parallel to y=x+3 18) through: (4,-4) parallel to y=3

## Step 1<br />The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.<br /><br />## Step 2<br />For a line to be parallel to another, their slopes must be equal. Therefore, the slope of the new line will be the same as the slope of the given line.<br /><br />## Step 3<br />The y-intercept of the new line can be found by substituting the given point into the equation \(y = mx + b\) and solving for \(b\).<br /><br />## Step 4<br />For the line -\frac{3}{4}x\), the slope is \(-\frac{3}{4}\). Substituting the point (4, -1) into the equation gives \(-1 = -\frac{3}{4} * 4 + b\), which simplifies to \(b = 2\).<br /><br />## Step 5<br />For the line parallel to \(y = \frac{1}{4}x - 4\), the slope is \(\frac{1}{4}\). Substituting the point (4, 5) into the equation gives \(5 = \frac{1}{4} * 4 + b\), which simplifies to \(b = 4\).<br /><br />## Step 6<br />For the line parallel to \(y = x + 3\), the slope is 1. Substituting the point (-2, -5(-5 = 1 * -2 + b\), which simplifies to \(b = -3\).<br /><br />## Step 7<br />For the line parallel to \(y = 3\), the slope is 0. Substituting the point (4, -4) into the equation gives \(-4 = 0 * 4 + b\), which simplifies to \(b = -4\).