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

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

Explanation:

x-intercept is when y = 0 → (-4, 0)

y-intercept is when x = 0 → (0, 3)

`\sf slope\:(m)=(change\:in\:y)/(change\:in\:x)=(3-0)/(0-(-4))=\frac34`

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=\frac34(x-(-4))`

`\implies \sf y=\frac34(x+4)`

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

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

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