Select all the equations that represent a line passing through the point (-2,5) with a slope of 4 y-5=4(x+2) y+5=4(x-2) y+2=4(x-5) 4x-y=-13 4x-y=13 2x-5y=4

## Step 1<br />The problem asks us to identify the equations that represent a line passing through the point (-2,5) with a slope of 4. The point-slope form of a line is given by the equation \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.<br /><br />## Step 2<br />Let's apply this formula to the given point (-2,5) and slope 4. Substituting these values into the formula, we get \(y - 5 = 4(x + 2)\).<br /><br />## Step 3<br />Next, we need to rearrange this equation into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.<br /><br />## Step 4<br />Rearranging the equation, we get \(y = 4x + 13\).<br /><br />## Step 5<br />Now, we need to compare this equation with the given options. The equations that represent the same line as \(y = 4x + 13\) are the ones that have the same slope and y-intercept.<br /><br />## Step 6<br />The equation \(y - 5 = 4(x + 2)\) can be rearranged to \(y = 4x + 13\), which is the same as our derived equation.<br /><br />## Step 7<br />The equation \(4x - y = -13\) can be rearranged to \(y = 4x + 13\), which is also the same as our derived equation.<br /><br />## Step 8<br />The other equations do not match our derived equation, so they do not represent the same line.