Question

in a certain urban area, the relationship between number of students, x in thousands, and the umber of schools, y , has an x-intercept of -4 and a y-intercept of 3. Write an equation for this relationship in standard form

Answer 1

Answer:

$\sf -3x+4y=12$

Step-by-step explanation:

x-intercept is when y = 0   →   (-4, 0)

y-intercept is when x = 0   →   (0, 3)

$\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{3-0}{0-(-4)}=\dfrac34$

Substitute one of the points and the found slope into the point-slope form of a linear equation:

$\implies \sf y-y_1=m(x-x_1)$

$\implies \sf y-0=\dfrac34(x-(-4))$

$\implies \sf y=\dfrac34(x+4)$

$\implies \sf 4y=3(x+4)$

$\implies \sf 4y=3x+12$

$\implies \sf -3x+4y=12$