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