Question

what is an equation of the line that is perpendicular to y-3=-4(x+2) and passes through the point (-5,7)

Answer 1

The equation of the line that is perpendicular to y-3=-4(x+2) and passes through (-5,7) is y = ¼x + 7.25.

Step-by-step explanation:

To find an equation of the line that is perpendicular to y - 3 = -4(x + 2) and passes through the point (-5,7), we need to determine the slope of the original line and then find the perpendicular slope. The original slope is -4. A perpendicular line would have the reciprocal positive slope, which is ¼. Using the slope-intercept form y = mx + b and the given point to solve for b, we plug in the coordinates of the point to get 7 = ¼(-5) + b. Solving for b, we find that it equals 7 + ⅔ = 7.25. The equation of the perpendicular line is therefore y = ¼x + 7.25.

Answer 2

Answer:remember that perpendicular lines have slopes that multiply to -1

y-y_1=m(x-x_1) is point-slope form

in point-slope form, it passes through the point (x_1,y_1) and has a slope of m

we want to find the equaiton of the line that is perpendicular to y-3=-4(x+2) and passes through (-5,7)

we need the slope

y-3=-4(x+2)

the slope is -4, but we want perpendicular so

-4 times what=-1?

divide both sides by -4

what=1/4

so the slope of our mystery line is 1/4 and it passe through (-5,7)

so we can write in point slope form as y-7=\frac{1}{4}(x-(-5)) or y-7=\frac{1}{4}(x+5)

the equation is y-7=\frac{1}{4}(x+5)

Step-by-step explanation:

act like it's a fraction you multiply the top number by the bottom number (numerator and the denominator)and then the other but it is keep change flip the same way with the first numbers