Question

Find an equation for the line which passes through (-1,3) and is perpendicular to the line containing (0,3) and (4,7). The equation of the line is . (Simplify your answer. Type your answer in slope-intercept form.)

Answer 1

Answer:

Equation of the line is y = -x + 4

Step-by-step explanation:

When the two lines having their slopes $m_{1}$ and $m_{2}$ are perpendicular to each other then $m_{1}\times m_{2}=-1$

If $m_{1}$ is the slope of the line passing through two points (0, 3) and (4, 7) then

$m_{1}=\frac{y-y'}{x-x'}$

= $\frac{7-3}{4-0}$

= 1

Now slope of the second line perpendicular to first line will be

$m_{2}$ = $-\frac{1}{m_{2} }$

$m_{2}$ = -1

Slope intercept form of the equation of a line is represented by

y = mx + c

where m = slope

c = y intercept

Since the line is passing through (-1, 3) and slope = -1, therefore,

3 = -1 + c

c = 4

Now we plug in these values in the equation.

y = -x + 4

Equation of the line is y = -x + 4