Provide the slope-intercept form of the equation for the line perpendicular to –7x + 5y = 12 that passes through the point (–7, 4). Choose an answer: y = x y = –7x + 4 y = x/7 + 4 y = –7x – 4

To find the slope-intercept form of the equation of the line that is perpendicular to –7x + 5y = 12 and contains the point P(–7, 4), we will go through several steps.

Step 1: Find the slope of the given line. The equation provided is in standard form. First, convert it to slope-intercept form (y = mx + b) to easily find the slope.

Starting with: –7x + 5y = 12

Add 7x to both sides to isolate the y term: 5y = 7x + 12

Divide all terms by 5 to solve for y: y = (7/5)x + 12/5

Now the equation is in slope-intercept form, and we can see that the slope (m) of the given line is 7/5.

Step 2: Determine the slope of the line perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals of each other. So if the slope of one line is 7/5, then the slope of a line perpendicular to it will be -5/7.

Step 3: Use the slope of the perpendicular line and the point P(–7, 4) to write the equation. Since the slope (m) of the perpendicular line is -5/7 and the point it passes through is P(–7, 4), we can use the point-slope form to write the equation of the line. Point-slope form is y - y1 = m(x - x1). Plugging in our values we get: y - 4 = (-5/7)(x - (-7))

Simplify the equation: y - 4 = (-5/7)(x + 7)

Now, we can convert this to slope-intercept form by distributing the slope and then isolating y.

Step 4: Distribute the slope and solve for y to get the slope-intercept form. y - 4 = (-5/7)x - (5/7)*7 y - 4 = (-5/7)x - 5

Add 4 to both sides: y = (-5/7)x - 1